--- _id: '8185' abstract: - lang: eng text: "In this paper we study envy-free division problems. The classical approach to some of such problems, used by David Gale, reduces to considering continuous maps of a simplex to itself and finding sufficient conditions when this map hits the center of the simplex. The mere continuity is not sufficient for such a conclusion, the usual assumption (for example, in the Knaster--Kuratowski--Mazurkiewicz and the Gale theorem) is a certain boundary condition.\r\n We follow Erel Segal-Halevi, Fr\\'ed\\'eric Meunier, and Shira Zerbib, and replace the boundary condition by another assumption, which has the economic meaning of possibility for a player to prefer an empty part in the segment\r\npartition problem. We solve the problem positively when $n$, the number of players that divide the segment, is a prime power, and we provide counterexamples for every $n$ which is not a prime power. We also provide counterexamples relevant to a wider class of fair or envy-free partition problems when $n$ is odd and not a prime power." article_number: '1907.11183' article_processing_charge: No author: - first_name: Sergey full_name: Avvakumov, Sergey id: 3827DAC8-F248-11E8-B48F-1D18A9856A87 last_name: Avvakumov - first_name: Roman full_name: Karasev, Roman last_name: Karasev citation: ama: Avvakumov S, Karasev R. Envy-free division using mapping degree. arXiv. doi:10.48550/arXiv.1907.11183 apa: Avvakumov, S., & Karasev, R. (n.d.). Envy-free division using mapping degree. arXiv. https://doi.org/10.48550/arXiv.1907.11183 chicago: Avvakumov, Sergey, and Roman Karasev. “Envy-Free Division Using Mapping Degree.” ArXiv, n.d. https://doi.org/10.48550/arXiv.1907.11183. ieee: S. Avvakumov and R. Karasev, “Envy-free division using mapping degree,” arXiv. . ista: Avvakumov S, Karasev R. Envy-free division using mapping degree. arXiv, 1907.11183. mla: Avvakumov, Sergey, and Roman Karasev. “Envy-Free Division Using Mapping Degree.” ArXiv, 1907.11183, doi:10.48550/arXiv.1907.11183. short: S. Avvakumov, R. Karasev, ArXiv (n.d.). date_created: 2020-07-30T10:45:51Z date_published: 2019-07-25T00:00:00Z date_updated: 2023-09-07T13:12:17Z day: '25' department: - _id: UlWa doi: 10.48550/arXiv.1907.11183 external_id: arxiv: - '1907.11183' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1907.11183 month: '07' oa: 1 oa_version: Preprint project: - _id: 26611F5C-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P31312 name: Algorithms for Embeddings and Homotopy Theory publication: arXiv publication_status: submitted related_material: link: - relation: later_version url: https://doi.org/10.1112/mtk.12059 record: - id: '8156' relation: dissertation_contains status: public status: public title: Envy-free division using mapping degree type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2019' ... --- _id: '5986' abstract: - lang: eng text: "Given a triangulation of a point set in the plane, a flip deletes an edge e whose removal leaves a convex quadrilateral, and replaces e by the opposite diagonal of the quadrilateral. It is well known that any triangulation of a point set can be reconfigured to any other triangulation by some sequence of flips. We explore this question in the setting where each edge of a triangulation has a label, and a flip transfers the label of the removed edge to the new edge. It is not true that every labelled triangulation of a point set can be reconfigured to every other labelled triangulation via a sequence of flips, but we characterize when this is possible. There is an obvious necessary condition: for each label l, if edge e has label l in the first triangulation and edge f has label l in the second triangulation, then there must be some sequence of flips that moves label l from e to f, ignoring all other labels. Bose, Lubiw, Pathak and Verdonschot formulated the Orbit Conjecture, which states that this necessary condition is also sufficient, i.e. that all labels can be simultaneously mapped to their destination if and only if each label individually can be mapped to its destination. We prove this conjecture. Furthermore, we give a polynomial-time algorithm (with \U0001D442(\U0001D45B8) being a crude bound on the run-time) to find a sequence of flips to reconfigure one labelled triangulation to another, if such a sequence exists, and we prove an upper bound of \U0001D442(\U0001D45B7) on the length of the flip sequence. Our proof uses the topological result that the sets of pairwise non-crossing edges on a planar point set form a simplicial complex that is homeomorphic to a high-dimensional ball (this follows from a result of Orden and Santos; we give a different proof based on a shelling argument). The dual cell complex of this simplicial ball, called the flip complex, has the usual flip graph as its 1-skeleton. We use properties of the 2-skeleton of the flip complex to prove the Orbit Conjecture." article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Anna full_name: Lubiw, Anna last_name: Lubiw - first_name: Zuzana full_name: Masárová, Zuzana id: 45CFE238-F248-11E8-B48F-1D18A9856A87 last_name: Masárová orcid: 0000-0002-6660-1322 - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 citation: ama: Lubiw A, Masárová Z, Wagner U. A proof of the orbit conjecture for flipping edge-labelled triangulations. Discrete & Computational Geometry. 2019;61(4):880-898. doi:10.1007/s00454-018-0035-8 apa: Lubiw, A., Masárová, Z., & Wagner, U. (2019). A proof of the orbit conjecture for flipping edge-labelled triangulations. Discrete & Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-018-0035-8 chicago: Lubiw, Anna, Zuzana Masárová, and Uli Wagner. “A Proof of the Orbit Conjecture for Flipping Edge-Labelled Triangulations.” Discrete & Computational Geometry. Springer Nature, 2019. https://doi.org/10.1007/s00454-018-0035-8. ieee: A. Lubiw, Z. Masárová, and U. Wagner, “A proof of the orbit conjecture for flipping edge-labelled triangulations,” Discrete & Computational Geometry, vol. 61, no. 4. Springer Nature, pp. 880–898, 2019. ista: Lubiw A, Masárová Z, Wagner U. 2019. A proof of the orbit conjecture for flipping edge-labelled triangulations. Discrete & Computational Geometry. 61(4), 880–898. mla: Lubiw, Anna, et al. “A Proof of the Orbit Conjecture for Flipping Edge-Labelled Triangulations.” Discrete & Computational Geometry, vol. 61, no. 4, Springer Nature, 2019, pp. 880–98, doi:10.1007/s00454-018-0035-8. short: A. Lubiw, Z. Masárová, U. Wagner, Discrete & Computational Geometry 61 (2019) 880–898. date_created: 2019-02-14T11:54:08Z date_published: 2019-06-01T00:00:00Z date_updated: 2023-09-07T13:17:36Z day: '01' ddc: - '000' department: - _id: UlWa doi: 10.1007/s00454-018-0035-8 external_id: arxiv: - '1710.02741' isi: - '000466130000009' file: - access_level: open_access checksum: e1bff88f1d77001b53b78c485ce048d7 content_type: application/pdf creator: dernst date_created: 2019-02-14T11:57:22Z date_updated: 2020-07-14T12:47:14Z file_id: '5988' file_name: 2018_DiscreteGeometry_Lubiw.pdf file_size: 556276 relation: main_file file_date_updated: 2020-07-14T12:47:14Z has_accepted_license: '1' intvolume: ' 61' isi: 1 issue: '4' language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '06' oa: 1 oa_version: Published Version page: 880-898 project: - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Discrete & Computational Geometry publication_identifier: eissn: - 1432-0444 issn: - 0179-5376 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '683' relation: earlier_version status: public - id: '7944' relation: dissertation_contains status: public scopus_import: '1' status: public title: A proof of the orbit conjecture for flipping edge-labelled triangulations tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 61 year: '2019' ... --- _id: '6556' abstract: - lang: eng text: 'Motivated by fixed-parameter tractable (FPT) problems in computational topology, we consider the treewidth tw(M) of a compact, connected 3-manifold M, defined to be the minimum treewidth of the face pairing graph of any triangulation T of M. In this setting the relationship between the topology of a 3-manifold and its treewidth is of particular interest. First, as a corollary of work of Jaco and Rubinstein, we prove that for any closed, orientable 3-manifold M the treewidth tw(M) is at most 4g(M)-2, where g(M) denotes Heegaard genus of M. In combination with our earlier work with Wagner, this yields that for non-Haken manifolds the Heegaard genus and the treewidth are within a constant factor. Second, we characterize all 3-manifolds of treewidth one: These are precisely the lens spaces and a single other Seifert fibered space. Furthermore, we show that all remaining orientable Seifert fibered spaces over the 2-sphere or a non-orientable surface have treewidth two. In particular, for every spherical 3-manifold we exhibit a triangulation of treewidth at most two. Our results further validate the parameter of treewidth (and other related parameters such as cutwidth or congestion) to be useful for topological computing, and also shed more light on the scope of existing FPT-algorithms in the field.' alternative_title: - LIPIcs article_processing_charge: No author: - first_name: Kristóf full_name: Huszár, Kristóf id: 33C26278-F248-11E8-B48F-1D18A9856A87 last_name: Huszár orcid: 0000-0002-5445-5057 - first_name: Jonathan full_name: Spreer, Jonathan last_name: Spreer citation: ama: 'Huszár K, Spreer J. 3-manifold triangulations with small treewidth. In: 35th International Symposium on Computational Geometry. Vol 129. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019:44:1-44:20. doi:10.4230/LIPIcs.SoCG.2019.44' apa: 'Huszár, K., & Spreer, J. (2019). 3-manifold triangulations with small treewidth. In 35th International Symposium on Computational Geometry (Vol. 129, p. 44:1-44:20). Portland, Oregon, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2019.44' chicago: Huszár, Kristóf, and Jonathan Spreer. “3-Manifold Triangulations with Small Treewidth.” In 35th International Symposium on Computational Geometry, 129:44:1-44:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. https://doi.org/10.4230/LIPIcs.SoCG.2019.44. ieee: K. Huszár and J. Spreer, “3-manifold triangulations with small treewidth,” in 35th International Symposium on Computational Geometry, Portland, Oregon, United States, 2019, vol. 129, p. 44:1-44:20. ista: 'Huszár K, Spreer J. 2019. 3-manifold triangulations with small treewidth. 35th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 129, 44:1-44:20.' mla: Huszár, Kristóf, and Jonathan Spreer. “3-Manifold Triangulations with Small Treewidth.” 35th International Symposium on Computational Geometry, vol. 129, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 44:1-44:20, doi:10.4230/LIPIcs.SoCG.2019.44. short: K. Huszár, J. Spreer, in:, 35th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 44:1-44:20. conference: end_date: 2019-06-21 location: Portland, Oregon, United States name: 'SoCG: Symposium on Computational Geometry' start_date: 2019-06-18 date_created: 2019-06-11T20:09:57Z date_published: 2019-06-01T00:00:00Z date_updated: 2023-09-07T13:18:26Z day: '01' ddc: - '516' department: - _id: UlWa doi: 10.4230/LIPIcs.SoCG.2019.44 external_id: arxiv: - '1812.05528' file: - access_level: open_access checksum: 29d18c435368468aa85823dabb157e43 content_type: application/pdf creator: kschuh date_created: 2019-06-12T06:45:33Z date_updated: 2020-07-14T12:47:33Z file_id: '6557' file_name: 2019_LIPIcs-Huszar.pdf file_size: 905885 relation: main_file file_date_updated: 2020-07-14T12:47:33Z has_accepted_license: '1' intvolume: ' 129' keyword: - computational 3-manifold topology - fixed-parameter tractability - layered triangulations - structural graph theory - treewidth - cutwidth - Heegaard genus language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 44:1-44:20 publication: 35th International Symposium on Computational Geometry publication_identifier: isbn: - 978-3-95977-104-7 issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' related_material: record: - id: '8032' relation: part_of_dissertation status: public scopus_import: '1' status: public title: 3-manifold triangulations with small treewidth tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 129 year: '2019' ... --- _id: '7093' abstract: - lang: eng text: "In graph theory, as well as in 3-manifold topology, there exist several width-type parameters to describe how \"simple\" or \"thin\" a given graph or 3-manifold is. These parameters, such as pathwidth or treewidth for graphs, or the concept of thin position for 3-manifolds, play an important role when studying algorithmic problems; in particular, there is a variety of problems in computational 3-manifold topology - some of them known to be computationally hard in general - that become solvable in polynomial time as soon as the dual graph of the input triangulation has bounded treewidth.\r\nIn view of these algorithmic results, it is natural to ask whether every 3-manifold admits a triangulation of bounded treewidth. We show that this is not the case, i.e., that there exists an infinite family of closed 3-manifolds not admitting triangulations of bounded pathwidth or treewidth (the latter implies the former, but we present two separate proofs).\r\nWe derive these results from work of Agol, of Scharlemann and Thompson, and of Scharlemann, Schultens and Saito by exhibiting explicit connections between the topology of a 3-manifold M on the one hand and width-type parameters of the dual graphs of triangulations of M on the other hand, answering a question that had been raised repeatedly by researchers in computational 3-manifold topology. In particular, we show that if a closed, orientable, irreducible, non-Haken 3-manifold M has a triangulation of treewidth (resp. pathwidth) k then the Heegaard genus of M is at most 18(k+1) (resp. 4(3k+1))." article_processing_charge: No article_type: original author: - first_name: Kristóf full_name: Huszár, Kristóf id: 33C26278-F248-11E8-B48F-1D18A9856A87 last_name: Huszár orcid: 0000-0002-5445-5057 - first_name: Jonathan full_name: Spreer, Jonathan last_name: Spreer - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 citation: ama: Huszár K, Spreer J, Wagner U. On the treewidth of triangulated 3-manifolds. Journal of Computational Geometry. 2019;10(2):70–98. doi:10.20382/JOGC.V10I2A5 apa: Huszár, K., Spreer, J., & Wagner, U. (2019). On the treewidth of triangulated 3-manifolds. Journal of Computational Geometry. Computational Geometry Laborartoy. https://doi.org/10.20382/JOGC.V10I2A5 chicago: Huszár, Kristóf, Jonathan Spreer, and Uli Wagner. “On the Treewidth of Triangulated 3-Manifolds.” Journal of Computational Geometry. Computational Geometry Laborartoy, 2019. https://doi.org/10.20382/JOGC.V10I2A5. ieee: K. Huszár, J. Spreer, and U. Wagner, “On the treewidth of triangulated 3-manifolds,” Journal of Computational Geometry, vol. 10, no. 2. Computational Geometry Laborartoy, pp. 70–98, 2019. ista: Huszár K, Spreer J, Wagner U. 2019. On the treewidth of triangulated 3-manifolds. Journal of Computational Geometry. 10(2), 70–98. mla: Huszár, Kristóf, et al. “On the Treewidth of Triangulated 3-Manifolds.” Journal of Computational Geometry, vol. 10, no. 2, Computational Geometry Laborartoy, 2019, pp. 70–98, doi:10.20382/JOGC.V10I2A5. short: K. Huszár, J. Spreer, U. Wagner, Journal of Computational Geometry 10 (2019) 70–98. date_created: 2019-11-23T12:14:09Z date_published: 2019-11-01T00:00:00Z date_updated: 2023-09-07T13:18:26Z day: '01' ddc: - '514' department: - _id: UlWa doi: 10.20382/JOGC.V10I2A5 external_id: arxiv: - '1712.00434' file: - access_level: open_access checksum: c872d590d38d538404782bca20c4c3f5 content_type: application/pdf creator: khuszar date_created: 2019-11-23T12:35:16Z date_updated: 2020-07-14T12:47:49Z file_id: '7094' file_name: 479-1917-1-PB.pdf file_size: 857590 relation: main_file file_date_updated: 2020-07-14T12:47:49Z has_accepted_license: '1' intvolume: ' 10' issue: '2' language: - iso: eng month: '11' oa: 1 oa_version: Published Version page: 70–98 publication: Journal of Computational Geometry publication_identifier: issn: - 1920-180X publication_status: published publisher: Computational Geometry Laborartoy quality_controlled: '1' related_material: record: - id: '285' relation: earlier_version status: public - id: '8032' relation: part_of_dissertation status: public status: public title: On the treewidth of triangulated 3-manifolds tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 10 year: '2019' ... --- _id: '8184' abstract: - lang: eng text: "Denote by ∆N the N-dimensional simplex. A map f : ∆N → Rd is an almost r-embedding if fσ1∩. . .∩fσr = ∅ whenever σ1, . . . , σr are pairwise disjoint faces. A counterexample to the topological Tverberg conjecture asserts that if r is not a prime power and d ≥ 2r + 1, then there is an almost r-embedding ∆(d+1)(r−1) → Rd. This was improved by Blagojevi´c–Frick–Ziegler using a simple construction of higher-dimensional counterexamples by taking k-fold join power of lower-dimensional ones. We improve this further (for d large compared to r): If r is not a prime power and N := (d+ 1)r−r l\r\nd + 2 r + 1 m−2, then there is an almost r-embedding ∆N → Rd. For the r-fold van Kampen–Flores conjecture we also produce counterexamples which are stronger than previously known. Our proof is based on generalizations of the Mabillard–Wagner theorem on construction of almost r-embeddings from equivariant maps, and of the Ozaydin theorem on existence of equivariant maps. " acknowledgement: We would like to thank F. Frick for helpful discussions article_number: '1908.08731' article_processing_charge: No author: - first_name: Sergey full_name: Avvakumov, Sergey id: 3827DAC8-F248-11E8-B48F-1D18A9856A87 last_name: Avvakumov - first_name: R. full_name: Karasev, R. last_name: Karasev - first_name: A. full_name: Skopenkov, A. last_name: Skopenkov citation: ama: Avvakumov S, Karasev R, Skopenkov A. Stronger counterexamples to the topological Tverberg conjecture. arXiv. apa: Avvakumov, S., Karasev, R., & Skopenkov, A. (n.d.). Stronger counterexamples to the topological Tverberg conjecture. arXiv. arXiv. chicago: Avvakumov, Sergey, R. Karasev, and A. Skopenkov. “Stronger Counterexamples to the Topological Tverberg Conjecture.” ArXiv. arXiv, n.d. ieee: S. Avvakumov, R. Karasev, and A. Skopenkov, “Stronger counterexamples to the topological Tverberg conjecture,” arXiv. arXiv. ista: Avvakumov S, Karasev R, Skopenkov A. Stronger counterexamples to the topological Tverberg conjecture. arXiv, 1908.08731. mla: Avvakumov, Sergey, et al. “Stronger Counterexamples to the Topological Tverberg Conjecture.” ArXiv, 1908.08731, arXiv. short: S. Avvakumov, R. Karasev, A. Skopenkov, ArXiv (n.d.). date_created: 2020-07-30T10:45:34Z date_published: 2019-08-23T00:00:00Z date_updated: 2023-09-08T11:20:02Z day: '23' department: - _id: UlWa external_id: arxiv: - '1908.08731' isi: - '000986519600004' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1908.08731 month: '08' oa: 1 oa_version: Preprint project: - _id: 26611F5C-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P31312 name: Algorithms for Embeddings and Homotopy Theory publication: arXiv publication_status: submitted publisher: arXiv related_material: record: - id: '8156' relation: dissertation_contains status: public status: public title: Stronger counterexamples to the topological Tverberg conjecture type: preprint user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2019' ... --- _id: '6982' abstract: - lang: eng text: "We present an efficient algorithm for a problem in the interface between clustering and graph embeddings. An embedding ϕ : G → M of a graph G into a 2-manifold M maps the vertices in V(G) to distinct points and the edges in E(G) to interior-disjoint Jordan arcs between the corresponding vertices. In applications in clustering, cartography, and visualization, nearby vertices and edges are often bundled to the same point or overlapping arcs due to data compression or low resolution. This raises the computational problem of deciding whether a given map ϕ : G → M comes from an embedding. A map ϕ : G → M is a weak embedding if it can be perturbed into an embedding ψ ϵ : G → M with ‖ ϕ − ψ ϵ ‖ < ϵ for every ϵ > 0, where ‖.‖ is the unform norm.\r\nA polynomial-time algorithm for recognizing weak embeddings has recently been found by Fulek and Kynčl. It reduces the problem to solving a system of linear equations over Z2. It runs in O(n2ω)≤ O(n4.75) time, where ω ∈ [2,2.373) is the matrix multiplication exponent and n is the number of vertices and edges of G. We improve the running time to O(n log n). Our algorithm is also conceptually simpler: We perform a sequence of local operations that gradually “untangles” the image ϕ(G) into an embedding ψ(G) or reports that ϕ is not a weak embedding. It combines local constraints on the orientation of subgraphs directly, thereby eliminating the need for solving large systems of linear equations.\r\n" article_number: '50' article_type: original author: - first_name: Hugo full_name: Akitaya, Hugo last_name: Akitaya - first_name: Radoslav full_name: Fulek, Radoslav id: 39F3FFE4-F248-11E8-B48F-1D18A9856A87 last_name: Fulek orcid: 0000-0001-8485-1774 - first_name: Csaba full_name: Tóth, Csaba last_name: Tóth citation: ama: Akitaya H, Fulek R, Tóth C. Recognizing weak embeddings of graphs. ACM Transactions on Algorithms. 2019;15(4). doi:10.1145/3344549 apa: Akitaya, H., Fulek, R., & Tóth, C. (2019). Recognizing weak embeddings of graphs. ACM Transactions on Algorithms. ACM. https://doi.org/10.1145/3344549 chicago: Akitaya, Hugo, Radoslav Fulek, and Csaba Tóth. “Recognizing Weak Embeddings of Graphs.” ACM Transactions on Algorithms. ACM, 2019. https://doi.org/10.1145/3344549. ieee: H. Akitaya, R. Fulek, and C. Tóth, “Recognizing weak embeddings of graphs,” ACM Transactions on Algorithms, vol. 15, no. 4. ACM, 2019. ista: Akitaya H, Fulek R, Tóth C. 2019. Recognizing weak embeddings of graphs. ACM Transactions on Algorithms. 15(4), 50. mla: Akitaya, Hugo, et al. “Recognizing Weak Embeddings of Graphs.” ACM Transactions on Algorithms, vol. 15, no. 4, 50, ACM, 2019, doi:10.1145/3344549. short: H. Akitaya, R. Fulek, C. Tóth, ACM Transactions on Algorithms 15 (2019). date_created: 2019-11-04T15:45:17Z date_published: 2019-10-01T00:00:00Z date_updated: 2023-09-15T12:19:31Z day: '01' department: - _id: UlWa doi: 10.1145/3344549 external_id: arxiv: - '1709.09209' intvolume: ' 15' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1709.09209 month: '10' oa: 1 oa_version: Preprint project: - _id: 261FA626-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02281 name: Eliminating intersections in drawings of graphs publication: ACM Transactions on Algorithms publication_status: published publisher: ACM quality_controlled: '1' related_material: record: - id: '309' relation: earlier_version status: public scopus_import: 1 status: public title: Recognizing weak embeddings of graphs type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 15 year: '2019' ... --- _id: '6647' abstract: - lang: eng text: The Tverberg theorem is one of the cornerstones of discrete geometry. It states that, given a set X of at least (d+1)(r-1)+1 points in R^d, one can find a partition X=X_1 cup ... cup X_r of X, such that the convex hulls of the X_i, i=1,...,r, all share a common point. In this paper, we prove a strengthening of this theorem that guarantees a partition which, in addition to the above, has the property that the boundaries of full-dimensional convex hulls have pairwise nonempty intersections. Possible generalizations and algorithmic aspects are also discussed. As a concrete application, we show that any n points in the plane in general position span floor[n/3] vertex-disjoint triangles that are pairwise crossing, meaning that their boundaries have pairwise nonempty intersections; this number is clearly best possible. A previous result of Alvarez-Rebollar et al. guarantees floor[n/6] pairwise crossing triangles. Our result generalizes to a result about simplices in R^d,d >=2. alternative_title: - LIPIcs author: - first_name: Radoslav full_name: Fulek, Radoslav id: 39F3FFE4-F248-11E8-B48F-1D18A9856A87 last_name: Fulek orcid: 0000-0001-8485-1774 - first_name: Bernd full_name: Gärtner, Bernd last_name: Gärtner - first_name: Andrey full_name: Kupavskii, Andrey last_name: Kupavskii - first_name: Pavel full_name: Valtr, Pavel last_name: Valtr - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 citation: ama: 'Fulek R, Gärtner B, Kupavskii A, Valtr P, Wagner U. The crossing Tverberg theorem. In: 35th International Symposium on Computational Geometry. Vol 129. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019:38:1-38:13. doi:10.4230/LIPICS.SOCG.2019.38' apa: 'Fulek, R., Gärtner, B., Kupavskii, A., Valtr, P., & Wagner, U. (2019). The crossing Tverberg theorem. In 35th International Symposium on Computational Geometry (Vol. 129, p. 38:1-38:13). Portland, OR, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.SOCG.2019.38' chicago: Fulek, Radoslav, Bernd Gärtner, Andrey Kupavskii, Pavel Valtr, and Uli Wagner. “The Crossing Tverberg Theorem.” In 35th International Symposium on Computational Geometry, 129:38:1-38:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. https://doi.org/10.4230/LIPICS.SOCG.2019.38. ieee: R. Fulek, B. Gärtner, A. Kupavskii, P. Valtr, and U. Wagner, “The crossing Tverberg theorem,” in 35th International Symposium on Computational Geometry, Portland, OR, United States, 2019, vol. 129, p. 38:1-38:13. ista: 'Fulek R, Gärtner B, Kupavskii A, Valtr P, Wagner U. 2019. The crossing Tverberg theorem. 35th International Symposium on Computational Geometry. SoCG 2019: Symposium on Computational Geometry, LIPIcs, vol. 129, 38:1-38:13.' mla: Fulek, Radoslav, et al. “The Crossing Tverberg Theorem.” 35th International Symposium on Computational Geometry, vol. 129, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 38:1-38:13, doi:10.4230/LIPICS.SOCG.2019.38. short: R. Fulek, B. Gärtner, A. Kupavskii, P. Valtr, U. Wagner, in:, 35th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 38:1-38:13. conference: end_date: 2019-06-21 location: Portland, OR, United States name: 'SoCG 2019: Symposium on Computational Geometry' start_date: 2019-06-18 date_created: 2019-07-17T10:35:04Z date_published: 2019-06-01T00:00:00Z date_updated: 2023-12-13T12:03:35Z day: '01' ddc: - '000' - '510' department: - _id: UlWa doi: 10.4230/LIPICS.SOCG.2019.38 external_id: arxiv: - '1812.04911' file: - access_level: open_access checksum: d6d017f8b41291b94d102294fa96ae9c content_type: application/pdf creator: dernst date_created: 2019-07-24T06:54:52Z date_updated: 2020-07-14T12:47:35Z file_id: '6667' file_name: 2019_LIPICS_Fulek.pdf file_size: 559837 relation: main_file file_date_updated: 2020-07-14T12:47:35Z has_accepted_license: '1' intvolume: ' 129' language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 38:1-38:13 project: - _id: 261FA626-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02281 name: Eliminating intersections in drawings of graphs publication: 35th International Symposium on Computational Geometry publication_identifier: isbn: - '9783959771047' issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' related_material: record: - id: '13974' relation: later_version status: public scopus_import: 1 status: public title: The crossing Tverberg theorem tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 129 year: '2019' ... --- _id: '7950' abstract: - lang: eng text: "The input to the token swapping problem is a graph with vertices v1, v2, . . . , vn, and n tokens with labels 1,2, . . . , n, one on each vertex. The goal is to get token i to vertex vi for all i= 1, . . . , n using a minimum number of swaps, where a swap exchanges the tokens on the endpoints of an edge.Token swapping on a tree, also known as “sorting with a transposition tree,” is not known to be in P nor NP-complete. We present some partial results:\r\n1. An optimum swap sequence may need to perform a swap on a leaf vertex that has the correct token (a “happy leaf”), disproving a conjecture of Vaughan.\r\n2. Any algorithm that fixes happy leaves—as all known approximation algorithms for the problem do—has approximation factor at least 4/3. Furthermore, the two best-known 2-approximation algorithms have approximation factor exactly 2.\r\n3. A generalized problem—weighted coloured token swapping—is NP-complete on trees, but solvable in polynomial time on paths and stars. In this version, tokens and vertices \ have colours, and colours have weights. The goal is to get every token to a vertex of the same colour, and the cost of a swap is the sum of the weights of the two tokens involved." article_number: '1903.06981' article_processing_charge: No author: - first_name: Ahmad full_name: Biniaz, Ahmad last_name: Biniaz - first_name: Kshitij full_name: Jain, Kshitij last_name: Jain - first_name: Anna full_name: Lubiw, Anna last_name: Lubiw - first_name: Zuzana full_name: Masárová, Zuzana id: 45CFE238-F248-11E8-B48F-1D18A9856A87 last_name: Masárová orcid: 0000-0002-6660-1322 - first_name: Tillmann full_name: Miltzow, Tillmann last_name: Miltzow - first_name: Debajyoti full_name: Mondal, Debajyoti last_name: Mondal - first_name: Anurag Murty full_name: Naredla, Anurag Murty last_name: Naredla - first_name: Josef full_name: Tkadlec, Josef id: 3F24CCC8-F248-11E8-B48F-1D18A9856A87 last_name: Tkadlec orcid: 0000-0002-1097-9684 - first_name: Alexi full_name: Turcotte, Alexi last_name: Turcotte citation: ama: Biniaz A, Jain K, Lubiw A, et al. Token swapping on trees. arXiv. apa: Biniaz, A., Jain, K., Lubiw, A., Masárová, Z., Miltzow, T., Mondal, D., … Turcotte, A. (n.d.). Token swapping on trees. arXiv. chicago: Biniaz, Ahmad, Kshitij Jain, Anna Lubiw, Zuzana Masárová, Tillmann Miltzow, Debajyoti Mondal, Anurag Murty Naredla, Josef Tkadlec, and Alexi Turcotte. “Token Swapping on Trees.” ArXiv, n.d. ieee: A. Biniaz et al., “Token swapping on trees,” arXiv. . ista: Biniaz A, Jain K, Lubiw A, Masárová Z, Miltzow T, Mondal D, Naredla AM, Tkadlec J, Turcotte A. Token swapping on trees. arXiv, 1903.06981. mla: Biniaz, Ahmad, et al. “Token Swapping on Trees.” ArXiv, 1903.06981. short: A. Biniaz, K. Jain, A. Lubiw, Z. Masárová, T. Miltzow, D. Mondal, A.M. Naredla, J. Tkadlec, A. Turcotte, ArXiv (n.d.). date_created: 2020-06-08T12:25:25Z date_published: 2019-03-16T00:00:00Z date_updated: 2024-01-04T12:42:08Z day: '16' department: - _id: HeEd - _id: UlWa - _id: KrCh external_id: arxiv: - '1903.06981' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1903.06981 month: '03' oa: 1 oa_version: Preprint publication: arXiv publication_status: submitted related_material: record: - id: '7944' relation: dissertation_contains status: public - id: '12833' relation: later_version status: public status: public title: Token swapping on trees type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2019' ... --- _id: '185' abstract: - lang: eng text: We resolve in the affirmative conjectures of A. Skopenkov and Repovš (1998), and M. Skopenkov (2003) generalizing the classical Hanani-Tutte theorem to the setting of approximating maps of graphs on 2-dimensional surfaces by embeddings. Our proof of this result is constructive and almost immediately implies an efficient algorithm for testing whether a given piecewise linear map of a graph in a surface is approximable by an embedding. More precisely, an instance of this problem consists of (i) a graph G whose vertices are partitioned into clusters and whose inter-cluster edges are partitioned into bundles, and (ii) a region R of a 2-dimensional compact surface M given as the union of a set of pairwise disjoint discs corresponding to the clusters and a set of pairwise disjoint "pipes" corresponding to the bundles, connecting certain pairs of these discs. We are to decide whether G can be embedded inside M so that the vertices in every cluster are drawn in the corresponding disc, the edges in every bundle pass only through its corresponding pipe, and every edge crosses the boundary of each disc at most once. alternative_title: - Leibniz International Proceedings in Information, LIPIcs article_number: '39' author: - first_name: Radoslav full_name: Fulek, Radoslav id: 39F3FFE4-F248-11E8-B48F-1D18A9856A87 last_name: Fulek orcid: 0000-0001-8485-1774 - first_name: Jan full_name: Kynčl, Jan last_name: Kynčl citation: ama: 'Fulek R, Kynčl J. Hanani-Tutte for approximating maps of graphs. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018. doi:10.4230/LIPIcs.SoCG.2018.39' apa: 'Fulek, R., & Kynčl, J. (2018). Hanani-Tutte for approximating maps of graphs (Vol. 99). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.39' chicago: Fulek, Radoslav, and Jan Kynčl. “Hanani-Tutte for Approximating Maps of Graphs,” Vol. 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.39. ieee: 'R. Fulek and J. Kynčl, “Hanani-Tutte for approximating maps of graphs,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99.' ista: 'Fulek R, Kynčl J. 2018. Hanani-Tutte for approximating maps of graphs. SoCG: Symposium on Computational Geometry, Leibniz International Proceedings in Information, LIPIcs, vol. 99, 39.' mla: Fulek, Radoslav, and Jan Kynčl. Hanani-Tutte for Approximating Maps of Graphs. Vol. 99, 39, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, doi:10.4230/LIPIcs.SoCG.2018.39. short: R. Fulek, J. Kynčl, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. conference: end_date: 2018-06-14 location: Budapest, Hungary name: 'SoCG: Symposium on Computational Geometry' start_date: 2018-06-11 date_created: 2018-12-11T11:45:04Z date_published: 2018-01-01T00:00:00Z date_updated: 2021-01-12T06:53:36Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.4230/LIPIcs.SoCG.2018.39 file: - access_level: open_access checksum: f1b94f1a75b37c414a1f61d59fb2cd4c content_type: application/pdf creator: dernst date_created: 2018-12-17T12:33:52Z date_updated: 2020-07-14T12:45:19Z file_id: '5701' file_name: 2018_LIPIcs_Fulek.pdf file_size: 718857 relation: main_file file_date_updated: 2020-07-14T12:45:19Z has_accepted_license: '1' intvolume: ' 99' language: - iso: eng month: '01' oa: 1 oa_version: Published Version project: - _id: 261FA626-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02281 name: Eliminating intersections in drawings of graphs publication_identifier: isbn: - 978-3-95977-066-8 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik publist_id: '7735' quality_controlled: '1' scopus_import: 1 status: public title: Hanani-Tutte for approximating maps of graphs tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 99 year: '2018' ... --- _id: '186' abstract: - lang: eng text: 'A drawing of a graph on a surface is independently even if every pair of nonadjacent edges in the drawing crosses an even number of times. The ℤ2-genus of a graph G is the minimum g such that G has an independently even drawing on the orientable surface of genus g. An unpublished result by Robertson and Seymour implies that for every t, every graph of sufficiently large genus contains as a minor a projective t × t grid or one of the following so-called t-Kuratowski graphs: K3, t, or t copies of K5 or K3,3 sharing at most 2 common vertices. We show that the ℤ2-genus of graphs in these families is unbounded in t; in fact, equal to their genus. Together, this implies that the genus of a graph is bounded from above by a function of its ℤ2-genus, solving a problem posed by Schaefer and Štefankovič, and giving an approximate version of the Hanani-Tutte theorem on orientable surfaces.' alternative_title: - LIPIcs article_processing_charge: No author: - first_name: Radoslav full_name: Fulek, Radoslav id: 39F3FFE4-F248-11E8-B48F-1D18A9856A87 last_name: Fulek orcid: 0000-0001-8485-1774 - first_name: Jan full_name: Kynčl, Jan last_name: Kynčl citation: ama: 'Fulek R, Kynčl J. The ℤ2-Genus of Kuratowski minors. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018:40.1-40.14. doi:10.4230/LIPIcs.SoCG.2018.40' apa: 'Fulek, R., & Kynčl, J. (2018). The ℤ2-Genus of Kuratowski minors (Vol. 99, p. 40.1-40.14). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.40' chicago: Fulek, Radoslav, and Jan Kynčl. “The ℤ2-Genus of Kuratowski Minors,” 99:40.1-40.14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.40. ieee: 'R. Fulek and J. Kynčl, “The ℤ2-Genus of Kuratowski minors,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99, p. 40.1-40.14.' ista: 'Fulek R, Kynčl J. 2018. The ℤ2-Genus of Kuratowski minors. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 99, 40.1-40.14.' mla: Fulek, Radoslav, and Jan Kynčl. The ℤ2-Genus of Kuratowski Minors. Vol. 99, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 40.1-40.14, doi:10.4230/LIPIcs.SoCG.2018.40. short: R. Fulek, J. Kynčl, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 40.1-40.14. conference: end_date: 2018-06-14 location: Budapest, Hungary name: 'SoCG: Symposium on Computational Geometry' start_date: 2018-06-11 date_created: 2018-12-11T11:45:05Z date_published: 2018-06-11T00:00:00Z date_updated: 2023-08-14T12:43:51Z day: '11' department: - _id: UlWa doi: 10.4230/LIPIcs.SoCG.2018.40 external_id: arxiv: - '1803.05085' intvolume: ' 99' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1803.05085 month: '06' oa: 1 oa_version: Submitted Version page: 40.1 - 40.14 project: - _id: 261FA626-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02281 name: Eliminating intersections in drawings of graphs publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik publist_id: '7734' quality_controlled: '1' related_material: record: - id: '11593' relation: later_version status: public scopus_import: '1' status: public title: The ℤ2-Genus of Kuratowski minors type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 99 year: '2018' ... --- _id: '433' abstract: - lang: eng text: 'A thrackle is a graph drawn in the plane so that every pair of its edges meet exactly once: either at a common end vertex or in a proper crossing. We prove that any thrackle of n vertices has at most 1.3984n edges. Quasi-thrackles are defined similarly, except that every pair of edges that do not share a vertex are allowed to cross an odd number of times. It is also shown that the maximum number of edges of a quasi-thrackle on n vertices is 3/2(n-1), and that this bound is best possible for infinitely many values of n.' alternative_title: - LNCS author: - first_name: Radoslav full_name: Fulek, Radoslav id: 39F3FFE4-F248-11E8-B48F-1D18A9856A87 last_name: Fulek orcid: 0000-0001-8485-1774 - first_name: János full_name: Pach, János last_name: Pach citation: ama: 'Fulek R, Pach J. Thrackles: An improved upper bound. In: Vol 10692. Springer; 2018:160-166. doi:10.1007/978-3-319-73915-1_14' apa: 'Fulek, R., & Pach, J. (2018). Thrackles: An improved upper bound (Vol. 10692, pp. 160–166). Presented at the GD 2017: Graph Drawing and Network Visualization, Boston, MA, United States: Springer. https://doi.org/10.1007/978-3-319-73915-1_14' chicago: 'Fulek, Radoslav, and János Pach. “Thrackles: An Improved Upper Bound,” 10692:160–66. Springer, 2018. https://doi.org/10.1007/978-3-319-73915-1_14.' ieee: 'R. Fulek and J. Pach, “Thrackles: An improved upper bound,” presented at the GD 2017: Graph Drawing and Network Visualization, Boston, MA, United States, 2018, vol. 10692, pp. 160–166.' ista: 'Fulek R, Pach J. 2018. Thrackles: An improved upper bound. GD 2017: Graph Drawing and Network Visualization, LNCS, vol. 10692, 160–166.' mla: 'Fulek, Radoslav, and János Pach. Thrackles: An Improved Upper Bound. Vol. 10692, Springer, 2018, pp. 160–66, doi:10.1007/978-3-319-73915-1_14.' short: R. Fulek, J. Pach, in:, Springer, 2018, pp. 160–166. conference: end_date: 2017-09-27 location: Boston, MA, United States name: 'GD 2017: Graph Drawing and Network Visualization' start_date: 201-09-25 date_created: 2018-12-11T11:46:27Z date_published: 2018-01-21T00:00:00Z date_updated: 2023-08-24T14:39:32Z day: '21' department: - _id: UlWa doi: 10.1007/978-3-319-73915-1_14 external_id: arxiv: - '1708.08037' intvolume: ' 10692' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1708.08037 month: '01' oa: 1 oa_version: Submitted Version page: 160 - 166 publication_status: published publisher: Springer publist_id: '7390' quality_controlled: '1' related_material: record: - id: '5857' relation: later_version status: public scopus_import: 1 status: public title: 'Thrackles: An improved upper bound' type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 10692 year: '2018' ... --- _id: '184' abstract: - lang: eng text: We prove that for every d ≥ 2, deciding if a pure, d-dimensional, simplicial complex is shellable is NP-hard, hence NP-complete. This resolves a question raised, e.g., by Danaraj and Klee in 1978. Our reduction also yields that for every d ≥ 2 and k ≥ 0, deciding if a pure, d-dimensional, simplicial complex is k-decomposable is NP-hard. For d ≥ 3, both problems remain NP-hard when restricted to contractible pure d-dimensional complexes. acknowledgement: 'Partially supported by the project EMBEDS II (CZ: 7AMB17FR029, FR: 38087RM) of Czech-French collaboration.' alternative_title: - Leibniz International Proceedings in Information, LIPIcs author: - first_name: Xavier full_name: Goaoc, Xavier last_name: Goaoc - first_name: Pavel full_name: Paták, Pavel last_name: Paták - first_name: Zuzana full_name: Patakova, Zuzana id: 48B57058-F248-11E8-B48F-1D18A9856A87 last_name: Patakova orcid: 0000-0002-3975-1683 - first_name: Martin full_name: Tancer, Martin id: 38AC689C-F248-11E8-B48F-1D18A9856A87 last_name: Tancer orcid: 0000-0002-1191-6714 - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 citation: ama: 'Goaoc X, Paták P, Patakova Z, Tancer M, Wagner U. Shellability is NP-complete. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018:41:1-41:16. doi:10.4230/LIPIcs.SoCG.2018.41' apa: 'Goaoc, X., Paták, P., Patakova, Z., Tancer, M., & Wagner, U. (2018). Shellability is NP-complete (Vol. 99, p. 41:1-41:16). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.41' chicago: Goaoc, Xavier, Pavel Paták, Zuzana Patakova, Martin Tancer, and Uli Wagner. “Shellability Is NP-Complete,” 99:41:1-41:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.41. ieee: 'X. Goaoc, P. Paták, Z. Patakova, M. Tancer, and U. Wagner, “Shellability is NP-complete,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99, p. 41:1-41:16.' ista: 'Goaoc X, Paták P, Patakova Z, Tancer M, Wagner U. 2018. Shellability is NP-complete. SoCG: Symposium on Computational Geometry, Leibniz International Proceedings in Information, LIPIcs, vol. 99, 41:1-41:16.' mla: Goaoc, Xavier, et al. Shellability Is NP-Complete. Vol. 99, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 41:1-41:16, doi:10.4230/LIPIcs.SoCG.2018.41. short: X. Goaoc, P. Paták, Z. Patakova, M. Tancer, U. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 41:1-41:16. conference: end_date: 2018-06-14 location: Budapest, Hungary name: 'SoCG: Symposium on Computational Geometry' start_date: 2018-06-11 date_created: 2018-12-11T11:45:04Z date_published: 2018-06-11T00:00:00Z date_updated: 2023-09-06T11:10:57Z day: '11' ddc: - '516' - '000' department: - _id: UlWa doi: 10.4230/LIPIcs.SoCG.2018.41 file: - access_level: open_access checksum: d12bdd60f04a57307867704b5f930afd content_type: application/pdf creator: dernst date_created: 2018-12-17T16:35:02Z date_updated: 2020-07-14T12:45:18Z file_id: '5725' file_name: 2018_LIPIcs_Goaoc.pdf file_size: 718414 relation: main_file file_date_updated: 2020-07-14T12:45:18Z has_accepted_license: '1' intvolume: ' 99' language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 41:1 - 41:16 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik publist_id: '7736' quality_controlled: '1' related_material: record: - id: '7108' relation: later_version status: public scopus_import: 1 status: public title: Shellability is NP-complete tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 99 year: '2018' ... --- _id: '285' abstract: - lang: eng text: In graph theory, as well as in 3-manifold topology, there exist several width-type parameters to describe how "simple" or "thin" a given graph or 3-manifold is. These parameters, such as pathwidth or treewidth for graphs, or the concept of thin position for 3-manifolds, play an important role when studying algorithmic problems; in particular, there is a variety of problems in computational 3-manifold topology - some of them known to be computationally hard in general - that become solvable in polynomial time as soon as the dual graph of the input triangulation has bounded treewidth. In view of these algorithmic results, it is natural to ask whether every 3-manifold admits a triangulation of bounded treewidth. We show that this is not the case, i.e., that there exists an infinite family of closed 3-manifolds not admitting triangulations of bounded pathwidth or treewidth (the latter implies the former, but we present two separate proofs). We derive these results from work of Agol and of Scharlemann and Thompson, by exhibiting explicit connections between the topology of a 3-manifold M on the one hand and width-type parameters of the dual graphs of triangulations of M on the other hand, answering a question that had been raised repeatedly by researchers in computational 3-manifold topology. In particular, we show that if a closed, orientable, irreducible, non-Haken 3-manifold M has a triangulation of treewidth (resp. pathwidth) k then the Heegaard genus of M is at most 48(k+1) (resp. 4(3k+1)). acknowledgement: Research of the second author was supported by the Einstein Foundation (project “Einstein Visiting Fellow Santos”) and by the Simons Foundation (“Simons Visiting Professors” program). alternative_title: - LIPIcs article_number: '46' article_processing_charge: No author: - first_name: Kristóf full_name: Huszár, Kristóf id: 33C26278-F248-11E8-B48F-1D18A9856A87 last_name: Huszár orcid: 0000-0002-5445-5057 - first_name: Jonathan full_name: Spreer, Jonathan last_name: Spreer - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 citation: ama: 'Huszár K, Spreer J, Wagner U. On the treewidth of triangulated 3-manifolds. In: Vol 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018. doi:10.4230/LIPIcs.SoCG.2018.46' apa: 'Huszár, K., Spreer, J., & Wagner, U. (2018). On the treewidth of triangulated 3-manifolds (Vol. 99). Presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2018.46' chicago: Huszár, Kristóf, Jonathan Spreer, and Uli Wagner. “On the Treewidth of Triangulated 3-Manifolds,” Vol. 99. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPIcs.SoCG.2018.46. ieee: 'K. Huszár, J. Spreer, and U. Wagner, “On the treewidth of triangulated 3-manifolds,” presented at the SoCG: Symposium on Computational Geometry, Budapest, Hungary, 2018, vol. 99.' ista: 'Huszár K, Spreer J, Wagner U. 2018. On the treewidth of triangulated 3-manifolds. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 99, 46.' mla: Huszár, Kristóf, et al. On the Treewidth of Triangulated 3-Manifolds. Vol. 99, 46, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, doi:10.4230/LIPIcs.SoCG.2018.46. short: K. Huszár, J. Spreer, U. Wagner, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. conference: end_date: 2018-06-14 location: Budapest, Hungary name: 'SoCG: Symposium on Computational Geometry' start_date: 2018-06-11 date_created: 2018-12-11T11:45:37Z date_published: 2018-06-01T00:00:00Z date_updated: 2023-09-06T11:13:41Z day: '01' ddc: - '516' - '000' department: - _id: UlWa doi: 10.4230/LIPIcs.SoCG.2018.46 external_id: arxiv: - '1712.00434' file: - access_level: open_access checksum: 530d084116778135d5bffaa317479cac content_type: application/pdf creator: dernst date_created: 2018-12-17T15:32:38Z date_updated: 2020-07-14T12:45:51Z file_id: '5713' file_name: 2018_LIPIcs_Huszar.pdf file_size: 642522 relation: main_file file_date_updated: 2020-07-14T12:45:51Z has_accepted_license: '1' intvolume: ' 99' language: - iso: eng month: '06' oa: 1 oa_version: Submitted Version publication_identifier: issn: - '18688969' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik publist_id: '7614' quality_controlled: '1' related_material: record: - id: '7093' relation: later_version status: public scopus_import: 1 status: public title: On the treewidth of triangulated 3-manifolds tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 99 year: '2018' ... --- _id: '6774' abstract: - lang: eng text: "A central problem of algebraic topology is to understand the homotopy groups \ \U0001D70B\U0001D451(\U0001D44B) of a topological space X. For the computational version of the problem, it is well known that there is no algorithm to decide whether the fundamental group \U0001D70B1(\U0001D44B) of a given finite simplicial complex X is trivial. On the other hand, there are several algorithms that, given a finite simplicial complex X that is simply connected (i.e., with \U0001D70B1(\U0001D44B) \ trivial), compute the higher homotopy group \U0001D70B\U0001D451(\U0001D44B) \ for any given \U0001D451≥2 . However, these algorithms come with a caveat: They compute the isomorphism type of \U0001D70B\U0001D451(\U0001D44B) , \U0001D451≥2 \ as an abstract finitely generated abelian group given by generators and relations, but they work with very implicit representations of the elements of \U0001D70B\U0001D451(\U0001D44B) . Converting elements of this abstract group into explicit geometric maps from the d-dimensional sphere \U0001D446\U0001D451 to X has been one of the main unsolved problems in the emerging field of computational homotopy theory. Here we present an algorithm that, given a simply connected space X, computes \U0001D70B\U0001D451(\U0001D44B) \ and represents its elements as simplicial maps from a suitable triangulation of the d-sphere \U0001D446\U0001D451 to X. For fixed d, the algorithm runs in time exponential in size(\U0001D44B) , the number of simplices of X. Moreover, we prove that this is optimal: For every fixed \U0001D451≥2 , we construct a family of simply connected spaces X such that for any simplicial map representing a generator of \U0001D70B\U0001D451(\U0001D44B) , the size of the triangulation of \U0001D446\U0001D451 on which the map is defined, is exponential in size(\U0001D44B) ." article_type: original author: - first_name: Marek full_name: Filakovský, Marek id: 3E8AF77E-F248-11E8-B48F-1D18A9856A87 last_name: Filakovský - first_name: Peter full_name: Franek, Peter id: 473294AE-F248-11E8-B48F-1D18A9856A87 last_name: Franek orcid: 0000-0001-8878-8397 - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 - first_name: Stephan Y full_name: Zhechev, Stephan Y id: 3AA52972-F248-11E8-B48F-1D18A9856A87 last_name: Zhechev citation: ama: Filakovský M, Franek P, Wagner U, Zhechev SY. Computing simplicial representatives of homotopy group elements. Journal of Applied and Computational Topology. 2018;2(3-4):177-231. doi:10.1007/s41468-018-0021-5 apa: Filakovský, M., Franek, P., Wagner, U., & Zhechev, S. Y. (2018). Computing simplicial representatives of homotopy group elements. Journal of Applied and Computational Topology. Springer. https://doi.org/10.1007/s41468-018-0021-5 chicago: Filakovský, Marek, Peter Franek, Uli Wagner, and Stephan Y Zhechev. “Computing Simplicial Representatives of Homotopy Group Elements.” Journal of Applied and Computational Topology. Springer, 2018. https://doi.org/10.1007/s41468-018-0021-5. ieee: M. Filakovský, P. Franek, U. Wagner, and S. Y. Zhechev, “Computing simplicial representatives of homotopy group elements,” Journal of Applied and Computational Topology, vol. 2, no. 3–4. Springer, pp. 177–231, 2018. ista: Filakovský M, Franek P, Wagner U, Zhechev SY. 2018. Computing simplicial representatives of homotopy group elements. Journal of Applied and Computational Topology. 2(3–4), 177–231. mla: Filakovský, Marek, et al. “Computing Simplicial Representatives of Homotopy Group Elements.” Journal of Applied and Computational Topology, vol. 2, no. 3–4, Springer, 2018, pp. 177–231, doi:10.1007/s41468-018-0021-5. short: M. Filakovský, P. Franek, U. Wagner, S.Y. Zhechev, Journal of Applied and Computational Topology 2 (2018) 177–231. date_created: 2019-08-08T06:47:40Z date_published: 2018-12-01T00:00:00Z date_updated: 2023-09-07T13:10:36Z day: '01' ddc: - '514' department: - _id: UlWa doi: 10.1007/s41468-018-0021-5 file: - access_level: open_access checksum: cf9e7fcd2a113dd4828774fc75cdb7e8 content_type: application/pdf creator: dernst date_created: 2019-08-08T06:55:21Z date_updated: 2020-07-14T12:47:40Z file_id: '6775' file_name: 2018_JourAppliedComputTopology_Filakovsky.pdf file_size: 1056278 relation: main_file file_date_updated: 2020-07-14T12:47:40Z has_accepted_license: '1' intvolume: ' 2' issue: 3-4 language: - iso: eng month: '12' oa: 1 oa_version: Published Version page: 177-231 project: - _id: 25F8B9BC-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M01980 name: Robust invariants of Nonlinear Systems - _id: 3AC91DDA-15DF-11EA-824D-93A3E7B544D1 call_identifier: FWF name: FWF Open Access Fund publication: Journal of Applied and Computational Topology publication_identifier: eissn: - 2367-1734 issn: - 2367-1726 publication_status: published publisher: Springer quality_controlled: '1' related_material: record: - id: '6681' relation: dissertation_contains status: public status: public title: Computing simplicial representatives of homotopy group elements tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 2 year: '2018' ... --- _id: '5791' abstract: - lang: eng text: Due to data compression or low resolution, nearby vertices and edges of a graph drawing may be bundled to a common node or arc. We model such a “compromised” drawing by a piecewise linear map φ:G → ℝ. We wish to perturb φ by an arbitrarily small ε>0 into a proper drawing (in which the vertices are distinct points, any two edges intersect in finitely many points, and no three edges have a common interior point) that minimizes the number of crossings. An ε-perturbation, for every ε>0, is given by a piecewise linear map (Formula Presented), where with ||·|| is the uniform norm (i.e., sup norm). We present a polynomial-time solution for this optimization problem when G is a cycle and the map φ has no spurs (i.e., no two adjacent edges are mapped to overlapping arcs). We also show that the problem becomes NP-complete (i) when G is an arbitrary graph and φ has no spurs, and (ii) when φ may have spurs and G is a cycle or a union of disjoint paths. alternative_title: - LNCS article_processing_charge: No author: - first_name: Radoslav full_name: Fulek, Radoslav id: 39F3FFE4-F248-11E8-B48F-1D18A9856A87 last_name: Fulek orcid: 0000-0001-8485-1774 - first_name: Csaba D. full_name: Tóth, Csaba D. last_name: Tóth citation: ama: 'Fulek R, Tóth CD. Crossing minimization in perturbed drawings. In: Vol 11282. Springer; 2018:229-241. doi:10.1007/978-3-030-04414-5_16' apa: 'Fulek, R., & Tóth, C. D. (2018). Crossing minimization in perturbed drawings (Vol. 11282, pp. 229–241). Presented at the Graph Drawing and Network Visualization, Barcelona, Spain: Springer. https://doi.org/10.1007/978-3-030-04414-5_16' chicago: Fulek, Radoslav, and Csaba D. Tóth. “Crossing Minimization in Perturbed Drawings,” 11282:229–41. Springer, 2018. https://doi.org/10.1007/978-3-030-04414-5_16. ieee: R. Fulek and C. D. Tóth, “Crossing minimization in perturbed drawings,” presented at the Graph Drawing and Network Visualization, Barcelona, Spain, 2018, vol. 11282, pp. 229–241. ista: Fulek R, Tóth CD. 2018. Crossing minimization in perturbed drawings. Graph Drawing and Network Visualization, LNCS, vol. 11282, 229–241. mla: Fulek, Radoslav, and Csaba D. Tóth. Crossing Minimization in Perturbed Drawings. Vol. 11282, Springer, 2018, pp. 229–41, doi:10.1007/978-3-030-04414-5_16. short: R. Fulek, C.D. Tóth, in:, Springer, 2018, pp. 229–241. conference: end_date: 2018-09-28 location: Barcelona, Spain name: Graph Drawing and Network Visualization start_date: 2018-09-26 date_created: 2018-12-30T22:59:15Z date_published: 2018-12-18T00:00:00Z date_updated: 2023-09-11T12:49:55Z day: '18' department: - _id: UlWa doi: 10.1007/978-3-030-04414-5_16 external_id: arxiv: - '1808.07608' isi: - '000672802500016' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1808.07608 month: '12' oa: 1 oa_version: Preprint page: 229-241 publication_identifier: isbn: - '9783030044138' publication_status: published publisher: Springer quality_controlled: '1' scopus_import: '1' status: public title: Crossing minimization in perturbed drawings type: conference user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: '11282 ' year: '2018' ... --- _id: '425' abstract: - lang: eng text: 'We show that the following algorithmic problem is decidable: given a 2-dimensional simplicial complex, can it be embedded (topologically, or equivalently, piecewise linearly) in R3? By a known reduction, it suffices to decide the embeddability of a given triangulated 3-manifold X into the 3-sphere S3. The main step, which allows us to simplify X and recurse, is in proving that if X can be embedded in S3, then there is also an embedding in which X has a short meridian, that is, an essential curve in the boundary of X bounding a disk in S3 \ X with length bounded by a computable function of the number of tetrahedra of X.' article_number: '5' article_processing_charge: No article_type: original author: - first_name: Jiří full_name: Matoušek, Jiří last_name: Matoušek - first_name: Eric full_name: Sedgwick, Eric last_name: Sedgwick - first_name: Martin full_name: Tancer, Martin id: 38AC689C-F248-11E8-B48F-1D18A9856A87 last_name: Tancer orcid: 0000-0002-1191-6714 - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 citation: ama: Matoušek J, Sedgwick E, Tancer M, Wagner U. Embeddability in the 3-Sphere is decidable. Journal of the ACM. 2018;65(1). doi:10.1145/3078632 apa: Matoušek, J., Sedgwick, E., Tancer, M., & Wagner, U. (2018). Embeddability in the 3-Sphere is decidable. Journal of the ACM. ACM. https://doi.org/10.1145/3078632 chicago: Matoušek, Jiří, Eric Sedgwick, Martin Tancer, and Uli Wagner. “Embeddability in the 3-Sphere Is Decidable.” Journal of the ACM. ACM, 2018. https://doi.org/10.1145/3078632. ieee: J. Matoušek, E. Sedgwick, M. Tancer, and U. Wagner, “Embeddability in the 3-Sphere is decidable,” Journal of the ACM, vol. 65, no. 1. ACM, 2018. ista: Matoušek J, Sedgwick E, Tancer M, Wagner U. 2018. Embeddability in the 3-Sphere is decidable. Journal of the ACM. 65(1), 5. mla: Matoušek, Jiří, et al. “Embeddability in the 3-Sphere Is Decidable.” Journal of the ACM, vol. 65, no. 1, 5, ACM, 2018, doi:10.1145/3078632. short: J. Matoušek, E. Sedgwick, M. Tancer, U. Wagner, Journal of the ACM 65 (2018). date_created: 2018-12-11T11:46:24Z date_published: 2018-01-01T00:00:00Z date_updated: 2023-09-11T13:38:49Z day: '01' department: - _id: UlWa doi: 10.1145/3078632 ec_funded: 1 external_id: arxiv: - '1402.0815' isi: - '000425685900006' intvolume: ' 65' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1402.0815 month: '01' oa: 1 oa_version: Preprint project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Journal of the ACM publication_status: published publisher: ACM publist_id: '7398' quality_controlled: '1' related_material: record: - id: '2157' relation: earlier_version status: public scopus_import: '1' status: public title: Embeddability in the 3-Sphere is decidable type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 65 year: '2018' ... --- _id: '309' abstract: - lang: eng text: 'We present an efficient algorithm for a problem in the interface between clustering and graph embeddings. An embedding '' : G ! M of a graph G into a 2manifold M maps the vertices in V (G) to distinct points and the edges in E(G) to interior-disjoint Jordan arcs between the corresponding vertices. In applications in clustering, cartography, and visualization, nearby vertices and edges are often bundled to a common node or arc, due to data compression or low resolution. This raises the computational problem of deciding whether a given map '' : G ! M comes from an embedding. A map '' : G ! M is a weak embedding if it can be perturbed into an embedding ψ: G ! M with k'' "k < " for every " > 0. A polynomial-time algorithm for recognizing weak embeddings was recently found by Fulek and Kyncl [14], which reduces to solving a system of linear equations over Z2. It runs in O(n2!) O(n4:75) time, where 2:373 is the matrix multiplication exponent and n is the number of vertices and edges of G. We improve the running time to O(n log n). Our algorithm is also conceptually simpler than [14]: We perform a sequence of local operations that gradually "untangles" the image ''(G) into an embedding (G), or reports that '' is not a weak embedding. It generalizes a recent technique developed for the case that G is a cycle and the embedding is a simple polygon [1], and combines local constraints on the orientation of subgraphs directly, thereby eliminating the need for solving large systems of linear equations.' acknowledgement: '∗Research supported in part by the NSF awards CCF-1422311 and CCF-1423615, and the Science Without Borders program. The second author gratefully acknowledges support from Austrian Science Fund (FWF): M2281-N35.' article_processing_charge: No author: - first_name: Hugo full_name: Akitaya, Hugo last_name: Akitaya - first_name: Radoslav full_name: Fulek, Radoslav id: 39F3FFE4-F248-11E8-B48F-1D18A9856A87 last_name: Fulek orcid: 0000-0001-8485-1774 - first_name: Csaba full_name: Tóth, Csaba last_name: Tóth citation: ama: 'Akitaya H, Fulek R, Tóth C. Recognizing weak embeddings of graphs. In: ACM; 2018:274-292. doi:10.1137/1.9781611975031.20' apa: 'Akitaya, H., Fulek, R., & Tóth, C. (2018). Recognizing weak embeddings of graphs (pp. 274–292). Presented at the SODA: Symposium on Discrete Algorithms, New Orleans, LA, USA: ACM. https://doi.org/10.1137/1.9781611975031.20' chicago: Akitaya, Hugo, Radoslav Fulek, and Csaba Tóth. “Recognizing Weak Embeddings of Graphs,” 274–92. ACM, 2018. https://doi.org/10.1137/1.9781611975031.20. ieee: 'H. Akitaya, R. Fulek, and C. Tóth, “Recognizing weak embeddings of graphs,” presented at the SODA: Symposium on Discrete Algorithms, New Orleans, LA, USA, 2018, pp. 274–292.' ista: 'Akitaya H, Fulek R, Tóth C. 2018. Recognizing weak embeddings of graphs. SODA: Symposium on Discrete Algorithms, 274–292.' mla: Akitaya, Hugo, et al. Recognizing Weak Embeddings of Graphs. ACM, 2018, pp. 274–92, doi:10.1137/1.9781611975031.20. short: H. Akitaya, R. Fulek, C. Tóth, in:, ACM, 2018, pp. 274–292. conference: end_date: 2018-01-10 location: New Orleans, LA, USA name: 'SODA: Symposium on Discrete Algorithms' start_date: 2018-01-07 date_created: 2018-12-11T11:45:45Z date_published: 2018-01-01T00:00:00Z date_updated: 2023-09-15T12:19:32Z day: '01' department: - _id: UlWa doi: 10.1137/1.9781611975031.20 external_id: arxiv: - '1709.09209' isi: - '000483921200021' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1709.09209 month: '01' oa: 1 oa_version: Preprint page: 274 - 292 project: - _id: 261FA626-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02281 name: Eliminating intersections in drawings of graphs publication_status: published publisher: ACM publist_id: '7556' quality_controlled: '1' related_material: record: - id: '6982' relation: later_version status: public scopus_import: '1' status: public title: Recognizing weak embeddings of graphs type: conference user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2018' ... --- _id: '5960' abstract: - lang: eng text: In this paper we present a reliable method to verify the existence of loops along the uncertain trajectory of a robot, based on proprioceptive measurements only, within a bounded-error context. The loop closure detection is one of the key points in simultaneous localization and mapping (SLAM) methods, especially in homogeneous environments with difficult scenes recognitions. The proposed approach is generic and could be coupled with conventional SLAM algorithms to reliably reduce their computing burden, thus improving the localization and mapping processes in the most challenging environments such as unexplored underwater extents. To prove that a robot performed a loop whatever the uncertainties in its evolution, we employ the notion of topological degree that originates in the field of differential topology. We show that a verification tool based on the topological degree is an optimal method for proving robot loops. This is demonstrated both on datasets from real missions involving autonomous underwater vehicles and by a mathematical discussion. article_processing_charge: No author: - first_name: Simon full_name: Rohou, Simon last_name: Rohou - first_name: Peter full_name: Franek, Peter id: 473294AE-F248-11E8-B48F-1D18A9856A87 last_name: Franek orcid: 0000-0001-8878-8397 - first_name: Clément full_name: Aubry, Clément last_name: Aubry - first_name: Luc full_name: Jaulin, Luc last_name: Jaulin citation: ama: Rohou S, Franek P, Aubry C, Jaulin L. Proving the existence of loops in robot trajectories. The International Journal of Robotics Research. 2018;37(12):1500-1516. doi:10.1177/0278364918808367 apa: Rohou, S., Franek, P., Aubry, C., & Jaulin, L. (2018). Proving the existence of loops in robot trajectories. The International Journal of Robotics Research. SAGE Publications. https://doi.org/10.1177/0278364918808367 chicago: Rohou, Simon, Peter Franek, Clément Aubry, and Luc Jaulin. “Proving the Existence of Loops in Robot Trajectories.” The International Journal of Robotics Research. SAGE Publications, 2018. https://doi.org/10.1177/0278364918808367. ieee: S. Rohou, P. Franek, C. Aubry, and L. Jaulin, “Proving the existence of loops in robot trajectories,” The International Journal of Robotics Research, vol. 37, no. 12. SAGE Publications, pp. 1500–1516, 2018. ista: Rohou S, Franek P, Aubry C, Jaulin L. 2018. Proving the existence of loops in robot trajectories. The International Journal of Robotics Research. 37(12), 1500–1516. mla: Rohou, Simon, et al. “Proving the Existence of Loops in Robot Trajectories.” The International Journal of Robotics Research, vol. 37, no. 12, SAGE Publications, 2018, pp. 1500–16, doi:10.1177/0278364918808367. short: S. Rohou, P. Franek, C. Aubry, L. Jaulin, The International Journal of Robotics Research 37 (2018) 1500–1516. date_created: 2019-02-13T09:36:20Z date_published: 2018-10-24T00:00:00Z date_updated: 2023-09-19T10:41:59Z day: '24' department: - _id: UlWa doi: 10.1177/0278364918808367 external_id: arxiv: - '1712.01341' isi: - '000456881100004' intvolume: ' 37' isi: 1 issue: '12' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1712.01341 month: '10' oa: 1 oa_version: Preprint page: 1500-1516 publication: The International Journal of Robotics Research publication_identifier: eissn: - 1741-3176 issn: - 0278-3649 publication_status: published publisher: SAGE Publications quality_controlled: '1' scopus_import: '1' status: public title: Proving the existence of loops in robot trajectories type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 37 year: '2018' ... --- _id: '6355' abstract: - lang: eng text: We prove that any cyclic quadrilateral can be inscribed in any closed convex C1-curve. The smoothness condition is not required if the quadrilateral is a rectangle. article_number: e7 article_processing_charge: No author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Sergey full_name: Avvakumov, Sergey id: 3827DAC8-F248-11E8-B48F-1D18A9856A87 last_name: Avvakumov citation: ama: Akopyan A, Avvakumov S. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. 2018;6. doi:10.1017/fms.2018.7 apa: Akopyan, A., & Avvakumov, S. (2018). Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2018.7 chicago: Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma. Cambridge University Press, 2018. https://doi.org/10.1017/fms.2018.7. ieee: A. Akopyan and S. Avvakumov, “Any cyclic quadrilateral can be inscribed in any closed convex smooth curve,” Forum of Mathematics, Sigma, vol. 6. Cambridge University Press, 2018. ista: Akopyan A, Avvakumov S. 2018. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. 6, e7. mla: Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” Forum of Mathematics, Sigma, vol. 6, e7, Cambridge University Press, 2018, doi:10.1017/fms.2018.7. short: A. Akopyan, S. Avvakumov, Forum of Mathematics, Sigma 6 (2018). date_created: 2019-04-30T06:09:57Z date_published: 2018-05-31T00:00:00Z date_updated: 2023-09-19T14:50:12Z day: '31' ddc: - '510' department: - _id: UlWa - _id: HeEd - _id: JaMa doi: 10.1017/fms.2018.7 ec_funded: 1 external_id: arxiv: - '1712.10205' isi: - '000433915500001' file: - access_level: open_access checksum: 5a71b24ba712a3eb2e46165a38fbc30a content_type: application/pdf creator: dernst date_created: 2019-04-30T06:14:58Z date_updated: 2020-07-14T12:47:28Z file_id: '6356' file_name: 2018_ForumMahtematics_Akopyan.pdf file_size: 249246 relation: main_file file_date_updated: 2020-07-14T12:47:28Z has_accepted_license: '1' intvolume: ' 6' isi: 1 language: - iso: eng month: '05' oa: 1 oa_version: Published Version project: - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics publication: Forum of Mathematics, Sigma publication_identifier: issn: - 2050-5094 publication_status: published publisher: Cambridge University Press quality_controlled: '1' related_material: record: - id: '8156' relation: dissertation_contains status: public status: public title: Any cyclic quadrilateral can be inscribed in any closed convex smooth curve tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 6 year: '2018' ... --- _id: '742' abstract: - lang: eng text: 'We give a detailed and easily accessible proof of Gromov’s Topological Overlap Theorem. Let X be a finite simplicial complex or, more generally, a finite polyhedral cell complex of dimension d. Informally, the theorem states that if X has sufficiently strong higher-dimensional expansion properties (which generalize edge expansion of graphs and are defined in terms of cellular cochains of X) then X has the following topological overlap property: for every continuous map (Formula presented.) there exists a point (Formula presented.) that is contained in the images of a positive fraction (Formula presented.) of the d-cells of X. More generally, the conclusion holds if (Formula presented.) is replaced by any d-dimensional piecewise-linear manifold M, with a constant (Formula presented.) that depends only on d and on the expansion properties of X, but not on M.' article_processing_charge: Yes (via OA deal) author: - first_name: Dominic full_name: Dotterrer, Dominic last_name: Dotterrer - first_name: Tali full_name: Kaufman, Tali last_name: Kaufman - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 citation: ama: Dotterrer D, Kaufman T, Wagner U. On expansion and topological overlap. Geometriae Dedicata. 2018;195(1):307–317. doi:10.1007/s10711-017-0291-4 apa: Dotterrer, D., Kaufman, T., & Wagner, U. (2018). On expansion and topological overlap. Geometriae Dedicata. Springer. https://doi.org/10.1007/s10711-017-0291-4 chicago: Dotterrer, Dominic, Tali Kaufman, and Uli Wagner. “On Expansion and Topological Overlap.” Geometriae Dedicata. Springer, 2018. https://doi.org/10.1007/s10711-017-0291-4. ieee: D. Dotterrer, T. Kaufman, and U. Wagner, “On expansion and topological overlap,” Geometriae Dedicata, vol. 195, no. 1. Springer, pp. 307–317, 2018. ista: Dotterrer D, Kaufman T, Wagner U. 2018. On expansion and topological overlap. Geometriae Dedicata. 195(1), 307–317. mla: Dotterrer, Dominic, et al. “On Expansion and Topological Overlap.” Geometriae Dedicata, vol. 195, no. 1, Springer, 2018, pp. 307–317, doi:10.1007/s10711-017-0291-4. short: D. Dotterrer, T. Kaufman, U. Wagner, Geometriae Dedicata 195 (2018) 307–317. date_created: 2018-12-11T11:48:16Z date_published: 2018-08-01T00:00:00Z date_updated: 2023-09-27T12:29:57Z day: '01' ddc: - '514' - '516' department: - _id: UlWa doi: 10.1007/s10711-017-0291-4 external_id: isi: - '000437122700017' file: - access_level: open_access checksum: d2f70fc132156504aa4c626aa378a7ab content_type: application/pdf creator: kschuh date_created: 2019-01-15T13:44:05Z date_updated: 2020-07-14T12:47:58Z file_id: '5835' file_name: s10711-017-0291-4.pdf file_size: 412486 relation: main_file file_date_updated: 2020-07-14T12:47:58Z has_accepted_license: '1' intvolume: ' 195' isi: 1 issue: '1' language: - iso: eng month: '08' oa: 1 oa_version: Published Version page: 307–317 project: - _id: 25FA3206-B435-11E9-9278-68D0E5697425 grant_number: PP00P2_138948 name: 'Embeddings in Higher Dimensions: Algorithms and Combinatorics' publication: Geometriae Dedicata publication_status: published publisher: Springer publist_id: '6925' pubrep_id: '912' quality_controlled: '1' related_material: record: - id: '1378' relation: earlier_version status: public scopus_import: '1' status: public title: On expansion and topological overlap tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 195 year: '2018' ...