[{"supervisor":[{"id":"36690CA2-F248-11E8-B48F-1D18A9856A87","first_name":"Uli","orcid":"0000-0002-1494-0568","full_name":"Wagner, Uli","last_name":"Wagner"},{"full_name":"Spreer, Jonathan","last_name":"Spreer","first_name":"Jonathan"}],"title":"Combinatorial width parameters for 3-dimensional manifolds","file":[{"date_created":"2020-06-26T10:03:58Z","checksum":"bd8be6e4f1addc863dfcc0fad29ee9c3","relation":"main_file","creator":"khuszar","file_name":"Kristof_Huszar-Thesis.pdf","date_updated":"2020-07-14T12:48:08Z","access_level":"open_access","file_size":2637562,"content_type":"application/pdf","file_id":"8034"},{"access_level":"closed","date_updated":"2020-07-14T12:48:08Z","file_size":7163491,"content_type":"application/x-zip-compressed","file_id":"8035","creator":"khuszar","file_name":"Kristof_Huszar-Thesis-source.zip","date_created":"2020-06-26T10:10:06Z","relation":"source_file","checksum":"d5f8456202b32f4a77552ef47a2837d1"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"7093"},{"id":"6556","relation":"dissertation_contains","status":"public"}]},"article_processing_charge":"No","alternative_title":["IST Austria Thesis"],"month":"06","abstract":[{"text":"Algorithms in computational 3-manifold topology typically take a triangulation as an input and return topological information about the underlying 3-manifold. However, extracting the desired information from a triangulation (e.g., evaluating an invariant) is often computationally very expensive. In recent years this complexity barrier has been successfully tackled in some cases by importing ideas from the theory of parameterized algorithms into the realm of 3-manifolds. Various computationally hard problems were shown to be efficiently solvable for input triangulations that are sufficiently “tree-like.”\r\nIn this thesis we focus on the key combinatorial parameter in the above context: we consider the treewidth of a compact, orientable 3-manifold, i.e., the smallest treewidth of the dual graph of any triangulation thereof. By building on the work of Scharlemann–Thompson and Scharlemann–Schultens–Saito on generalized Heegaard splittings, and on the work of Jaco–Rubinstein on layered triangulations, we establish quantitative relations between the treewidth and classical topological invariants of a 3-manifold. In particular, among other results, we show that the treewidth of a closed, orientable, irreducible, non-Haken 3-manifold is always within a constant factor of its Heegaard genus.","lang":"eng"}],"publication_identifier":{"issn":["2663-337X"],"isbn":["978-3-99078-006-0"]},"type":"dissertation","doi":"10.15479/AT:ISTA:8032","publisher":"IST Austria","department":[{"_id":"UlWa"}],"license":"https://creativecommons.org/licenses/by/4.0/","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2020-06-26T10:00:36Z","oa":1,"_id":"8032","status":"public","file_date_updated":"2020-07-14T12:48:08Z","date_published":"2020-06-26T00:00:00Z","has_accepted_license":"1","citation":{"ama":"Huszár K. Combinatorial width parameters for 3-dimensional manifolds. 2020. doi:10.15479/AT:ISTA:8032","ista":"Huszár K. 2020. Combinatorial width parameters for 3-dimensional manifolds. IST Austria.","apa":"Huszár, K. (2020). *Combinatorial width parameters for 3-dimensional manifolds*. IST Austria. https://doi.org/10.15479/AT:ISTA:8032","chicago":"Huszár, Kristóf. “Combinatorial Width Parameters for 3-Dimensional Manifolds.” IST Austria, 2020. https://doi.org/10.15479/AT:ISTA:8032.","mla":"Huszár, Kristóf. *Combinatorial Width Parameters for 3-Dimensional Manifolds*. IST Austria, 2020, doi:10.15479/AT:ISTA:8032.","short":"K. Huszár, Combinatorial Width Parameters for 3-Dimensional Manifolds, IST Austria, 2020.","ieee":"K. Huszár, “Combinatorial width parameters for 3-dimensional manifolds,” IST Austria, 2020."},"year":"2020","author":[{"orcid":"0000-0002-5445-5057","first_name":"Kristóf","id":"33C26278-F248-11E8-B48F-1D18A9856A87","last_name":"Huszár","full_name":"Huszár, Kristóf"}],"page":"xviii+120","tmp":{"short":"CC BY (4.0)","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)"},"day":"26","acknowledged_ssus":[{"_id":"E-Lib"},{"_id":"CampIT"}],"oa_version":"Published Version","ddc":["514"],"publication_status":"published","date_updated":"2021-01-12T08:16:39Z","language":[{"iso":"eng"}]},{"month":"07","abstract":[{"text":"We present solutions to several problems originating from geometry and discrete mathematics: existence of equipartitions, maps without Tverberg multiple points, and inscribing quadrilaterals. Equivariant obstruction theory is the natural topological approach to these type of questions. However, for the specific problems we consider it had yielded only partial or no results. We get our results by complementing equivariant obstruction theory with other techniques from topology and geometry.","lang":"eng"}],"publication_identifier":{"unknown":["2663-337X"]},"type":"dissertation","doi":"10.15479/AT:ISTA:8156","publisher":"IST Austria","department":[{"_id":"UlWa"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","supervisor":[{"last_name":"Wagner","full_name":"Wagner, Uli","orcid":"0000-0002-1494-0568","first_name":"Uli","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"}],"title":"Topological methods in geometry and discrete mathematics","file":[{"relation":"source_file","date_created":"2020-07-27T12:44:51Z","creator":"savvakum","file_name":"source.zip","access_level":"closed","date_updated":"2020-07-27T12:44:51Z","file_id":"8178","content_type":"application/zip","file_size":1061740},{"success":1,"relation":"main_file","date_created":"2020-07-27T12:46:53Z","access_level":"open_access","date_updated":"2020-07-27T12:46:53Z","file_id":"8179","content_type":"application/pdf","file_size":1336501,"creator":"savvakum","file_name":"thesis_pdfa.pdf"}],"related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"6355"},{"relation":"part_of_dissertation","status":"public","id":"75"},{"status":"public","relation":"part_of_dissertation","id":"8182"},{"id":"8183","status":"public","relation":"part_of_dissertation"},{"id":"8184","relation":"part_of_dissertation","status":"public"},{"id":"8185","status":"public","relation":"part_of_dissertation"}]},"article_processing_charge":"No","alternative_title":["IST Austria Thesis"],"day":"24","oa_version":"Published Version","ddc":["514"],"publication_status":"published","date_updated":"2021-01-12T08:17:21Z","language":[{"iso":"eng"}],"date_created":"2020-07-23T09:51:29Z","oa":1,"_id":"8156","file_date_updated":"2020-07-27T12:46:53Z","status":"public","date_published":"2020-07-24T00:00:00Z","has_accepted_license":"1","citation":{"ieee":"S. Avvakumov, “Topological methods in geometry and discrete mathematics,” IST Austria, 2020.","mla":"Avvakumov, Sergey. *Topological Methods in Geometry and Discrete Mathematics*. IST Austria, 2020, doi:10.15479/AT:ISTA:8156.","short":"S. Avvakumov, Topological Methods in Geometry and Discrete Mathematics, IST Austria, 2020.","chicago":"Avvakumov, Sergey. “Topological Methods in Geometry and Discrete Mathematics.” IST Austria, 2020. https://doi.org/10.15479/AT:ISTA:8156.","ama":"Avvakumov S. Topological methods in geometry and discrete mathematics. 2020. doi:10.15479/AT:ISTA:8156","apa":"Avvakumov, S. (2020). *Topological methods in geometry and discrete mathematics*. IST Austria. https://doi.org/10.15479/AT:ISTA:8156","ista":"Avvakumov S. 2020. Topological methods in geometry and discrete mathematics. IST Austria."},"author":[{"id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","first_name":"Sergey","full_name":"Avvakumov, Sergey","last_name":"Avvakumov"}],"page":"119","year":"2020"},{"tmp":{"short":"CC BY-SA (4.0)","image":"/images/cc_by_sa.png","legal_code_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","name":"Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0)"},"keyword":["reconfiguration","reconfiguration graph","triangulations","flip","constrained triangulations","shellability","piecewise-linear balls","token swapping","trees","coloured weighted token swapping"],"day":"09","ddc":["516","514"],"oa_version":"Published Version","publication_status":"published","date_updated":"2021-01-12T08:16:11Z","language":[{"iso":"eng"}],"date_created":"2020-06-08T00:49:46Z","oa":1,"_id":"7944","status":"public","file_date_updated":"2020-07-14T12:48:05Z","has_accepted_license":"1","citation":{"ama":"Masárová Z. Reconfiguration problems. 2020. doi:10.15479/AT:ISTA:7944","apa":"Masárová, Z. (2020). *Reconfiguration problems*. IST Austria. https://doi.org/10.15479/AT:ISTA:7944","ista":"Masárová Z. 2020. Reconfiguration problems. IST Austria.","ieee":"Z. Masárová, “Reconfiguration problems,” IST Austria, 2020.","chicago":"Masárová, Zuzana. “Reconfiguration Problems.” IST Austria, 2020. https://doi.org/10.15479/AT:ISTA:7944.","mla":"Masárová, Zuzana. *Reconfiguration Problems*. IST Austria, 2020, doi:10.15479/AT:ISTA:7944.","short":"Z. Masárová, Reconfiguration Problems, IST Austria, 2020."},"date_published":"2020-06-09T00:00:00Z","author":[{"id":"45CFE238-F248-11E8-B48F-1D18A9856A87","first_name":"Zuzana","orcid":"0000-0002-6660-1322","last_name":"Masárová","full_name":"Masárová, Zuzana"}],"page":"160","year":"2020","abstract":[{"text":"This thesis considers two examples of reconfiguration problems: flipping edges in edge-labelled triangulations of planar point sets and swapping labelled tokens placed on vertices of a graph. In both cases the studied structures – all the triangulations of a given point set or all token placements on a given graph – can be thought of as vertices of the so-called reconfiguration graph, in which two vertices are adjacent if the corresponding structures differ by a single elementary operation – by a flip of a diagonal in a triangulation or by a swap of tokens on adjacent vertices, respectively. We study the reconfiguration of one instance of a structure into another via (shortest) paths in the reconfiguration graph.\r\n\r\nFor triangulations of point sets in which each edge has a unique label and a flip transfers the label from the removed edge to the new edge, we prove a polynomial-time testable condition, called the Orbit Theorem, that characterizes when two triangulations of the same point set lie in the same connected component of the reconfiguration graph. The condition was first conjectured by Bose, Lubiw, Pathak and Verdonschot. We additionally provide a polynomial time algorithm that computes a reconfiguring flip sequence, if it exists. Our proof of the Orbit Theorem uses topological properties of a certain high-dimensional cell complex that has the usual reconfiguration graph as its 1-skeleton.\r\n\r\nIn the context of token swapping on a tree graph, we make partial progress on the problem of finding shortest reconfiguration sequences. We disprove the so-called Happy Leaf Conjecture and demonstrate the importance of swapping tokens that are already placed at the correct vertices. We also prove that a generalization of the problem to weighted coloured token swapping is NP-hard on trees but solvable in polynomial time on paths and stars.","lang":"eng"}],"month":"06","type":"dissertation","doi":"10.15479/AT:ISTA:7944","publication_identifier":{"isbn":["978-3-99078-005-3"],"eissn":["2663-337X"]},"publisher":"IST Austria","department":[{"_id":"HeEd"},{"_id":"UlWa"}],"license":"https://creativecommons.org/licenses/by-sa/4.0/","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","supervisor":[{"id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568","first_name":"Uli","full_name":"Wagner, Uli","last_name":"Wagner"},{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"file":[{"date_created":"2020-06-08T00:34:00Z","checksum":"df688bc5a82b50baee0b99d25fc7b7f0","relation":"main_file","access_level":"open_access","date_updated":"2020-07-14T12:48:05Z","file_size":13661779,"content_type":"application/pdf","file_id":"7945","creator":"zmasarov","file_name":"THESIS_Zuzka_Masarova.pdf"},{"file_name":"THESIS_Zuzka_Masarova_SOURCE_FILES.zip","creator":"zmasarov","content_type":"application/zip","file_size":32184006,"file_id":"7946","date_updated":"2020-07-14T12:48:05Z","access_level":"closed","date_created":"2020-06-08T00:35:30Z","checksum":"45341a35b8f5529c74010b7af43ac188","relation":"source_file"}],"title":"Reconfiguration problems","related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"5986"},{"relation":"part_of_dissertation","status":"public","id":"7950"}]},"article_processing_charge":"No","alternative_title":["IST Austria Thesis"]},{"publisher":"IST Austria","doi":"10.15479/AT:ISTA:6681","type":"dissertation","publication_identifier":{"issn":["2663-337X"]},"abstract":[{"text":"The first part of the thesis considers the computational aspects of the homotopy groups πd(X) of a topological space X. It is well known that there is no algorithm to decide whether the fundamental group π1(X) 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 π1(X) trivial), compute the higher homotopy group πd(X) for any given d ≥ 2.\r\nHowever, these algorithms come with a caveat: They compute the isomorphism type of πd(X), d ≥ 2 as an abstract finitely generated abelian group given by generators and relations, but they work with very implicit representations of the elements of πd(X). We present an algorithm that, given a simply connected space X, computes πd(X) and represents its elements as simplicial maps from suitable triangulations of the d-sphere Sd to X. For fixed d, the algorithm runs in time exponential in size(X), the number of simplices of X. Moreover, we prove that this is optimal: For every fixed d ≥ 2,\r\nwe construct a family of simply connected spaces X such that for any simplicial map representing a generator of πd(X), the size of the triangulation of S d on which the map is defined, is exponential in size(X).\r\nIn the second part of the thesis, we prove that the following question is algorithmically undecidable for d < ⌊3(k+1)/2⌋, k ≥ 5 and (k, d) ̸= (5, 7), which covers essentially everything outside the meta-stable range: Given a finite simplicial complex K of dimension k, decide whether there exists a piecewise-linear (i.e., linear on an arbitrarily fine subdivision of K) embedding f : K ↪→ Rd of K into a d-dimensional Euclidean space.","lang":"eng"}],"month":"08","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"UlWa"}],"file":[{"date_created":"2019-08-07T13:02:50Z","checksum":"3231e7cbfca3b5687366f84f0a57a0c0","relation":"main_file","creator":"szhechev","file_name":"Stephan_Zhechev_thesis.pdf","date_updated":"2020-07-14T12:47:37Z","access_level":"open_access","content_type":"application/pdf","file_size":1464227,"file_id":"6771"},{"date_created":"2019-08-07T13:03:22Z","relation":"source_file","checksum":"85d65eb27b4377a9e332ee37a70f08b6","content_type":"application/octet-stream","file_size":303988,"file_id":"6772","access_level":"closed","date_updated":"2020-07-14T12:47:37Z","file_name":"Stephan_Zhechev_thesis.tex","creator":"szhechev"},{"file_name":"supplementary_material.zip","creator":"szhechev","content_type":"application/zip","file_size":1087004,"file_id":"6773","access_level":"closed","date_updated":"2020-07-14T12:47:37Z","date_created":"2019-08-07T13:03:34Z","checksum":"86b374d264ca2dd53e712728e253ee75","relation":"supplementary_material"}],"title":"Algorithmic aspects of homotopy theory and embeddability","supervisor":[{"last_name":"Wagner","full_name":"Wagner, Uli","first_name":"Uli","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"}],"alternative_title":["IST Austria Thesis"],"related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"6774"}]},"ddc":["514"],"oa_version":"Published Version","day":"08","tmp":{"short":"CC BY (4.0)","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)"},"language":[{"iso":"eng"}],"date_updated":"2021-01-12T08:08:57Z","publication_status":"published","_id":"6681","oa":1,"date_created":"2019-07-26T11:14:34Z","page":"104","author":[{"full_name":"Zhechev, Stephan Y","last_name":"Zhechev","id":"3AA52972-F248-11E8-B48F-1D18A9856A87","first_name":"Stephan Y"}],"year":"2019","citation":{"ama":"Zhechev SY. Algorithmic aspects of homotopy theory and embeddability. 2019. doi:10.15479/AT:ISTA:6681","ista":"Zhechev SY. 2019. Algorithmic aspects of homotopy theory and embeddability. IST Austria.","apa":"Zhechev, S. Y. (2019). *Algorithmic aspects of homotopy theory and embeddability*. IST Austria. https://doi.org/10.15479/AT:ISTA:6681","ieee":"S. Y. Zhechev, “Algorithmic aspects of homotopy theory and embeddability,” IST Austria, 2019.","short":"S.Y. Zhechev, Algorithmic Aspects of Homotopy Theory and Embeddability, IST Austria, 2019.","mla":"Zhechev, Stephan Y. *Algorithmic Aspects of Homotopy Theory and Embeddability*. IST Austria, 2019, doi:10.15479/AT:ISTA:6681.","chicago":"Zhechev, Stephan Y. “Algorithmic Aspects of Homotopy Theory and Embeddability.” IST Austria, 2019. https://doi.org/10.15479/AT:ISTA:6681."},"has_accepted_license":"1","date_published":"2019-08-08T00:00:00Z","status":"public","file_date_updated":"2020-07-14T12:47:37Z"},{"oa":1,"date_created":"2018-12-11T11:50:16Z","_id":"1123","has_accepted_license":"1","citation":{"ama":"Mabillard I. Eliminating higher-multiplicity intersections: an r-fold Whitney trick for the topological Tverberg conjecture. 2016.","ista":"Mabillard I. 2016. Eliminating higher-multiplicity intersections: an r-fold Whitney trick for the topological Tverberg conjecture. IST Austria.","apa":"Mabillard, I. (2016). *Eliminating higher-multiplicity intersections: an r-fold Whitney trick for the topological Tverberg conjecture*. IST Austria.","ieee":"I. Mabillard, “Eliminating higher-multiplicity intersections: an r-fold Whitney trick for the topological Tverberg conjecture,” IST Austria, 2016.","chicago":"Mabillard, Isaac. “Eliminating Higher-Multiplicity Intersections: An r-Fold Whitney Trick for the Topological Tverberg Conjecture.” IST Austria, 2016.","mla":"Mabillard, Isaac. *Eliminating Higher-Multiplicity Intersections: An r-Fold Whitney Trick for the Topological Tverberg Conjecture*. IST Austria, 2016.","short":"I. Mabillard, Eliminating Higher-Multiplicity Intersections: An r-Fold Whitney Trick for the Topological Tverberg Conjecture, IST Austria, 2016."},"date_published":"2016-08-01T00:00:00Z","status":"public","file_date_updated":"2021-02-22T11:36:34Z","page":"55","author":[{"first_name":"Isaac","id":"32BF9DAA-F248-11E8-B48F-1D18A9856A87","full_name":"Mabillard, Isaac","last_name":"Mabillard"}],"publist_id":"6237","year":"2016","ddc":["500"],"oa_version":"Published Version","day":"01","date_updated":"2021-02-23T00:00:07Z","publication_status":"published","language":[{"iso":"eng"}],"supervisor":[{"full_name":"Wagner, Uli","last_name":"Wagner","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1494-0568","first_name":"Uli"}],"file":[{"file_id":"6809","file_size":2227916,"content_type":"application/pdf","access_level":"closed","date_updated":"2019-08-13T08:45:27Z","file_name":"Thesis_final version_Mabillard_w_signature_page.pdf","creator":"dernst","relation":"main_file","checksum":"2d140cc924cd1b764544906fc22684ef","date_created":"2019-08-13T08:45:27Z"},{"checksum":"2d140cc924cd1b764544906fc22684ef","relation":"main_file","success":1,"date_created":"2021-02-22T11:36:34Z","access_level":"open_access","date_updated":"2021-02-22T11:36:34Z","file_id":"9178","content_type":"application/pdf","file_size":2227916,"creator":"dernst","file_name":"2016_Mabillard_Thesis.pdf"}],"title":"Eliminating higher-multiplicity intersections: an r-fold Whitney trick for the topological Tverberg conjecture","related_material":{"record":[{"id":"2159","status":"public","relation":"part_of_dissertation"}]},"alternative_title":["IST Austria Thesis"],"article_processing_charge":"No","type":"dissertation","abstract":[{"text":"Motivated by topological Tverberg-type problems in topological combinatorics and by classical\r\nresults about embeddings (maps without double points), we study the question whether a finite\r\nsimplicial complex K can be mapped into Rd without triple, quadruple, or, more generally, r-fold points (image points with at least r distinct preimages), for a given multiplicity r ≤ 2. In particular, we are interested in maps f : K → Rd that have no global r -fold intersection points, i.e., no r -fold points with preimages in r pairwise disjoint simplices of K , and we seek necessary and sufficient conditions for the existence of such maps.\r\n\r\nWe present higher-multiplicity analogues of several classical results for embeddings, in particular of the completeness of the Van Kampen obstruction for embeddability of k -dimensional\r\ncomplexes into R2k , k ≥ 3. Speciffically, we show that under suitable restrictions on the dimensions(viz., if dimK = (r ≥ 1)k and d = rk \\ for some k ≥ 3), a well-known deleted product criterion (DPC ) is not only necessary but also sufficient for the existence of maps without global r -fold points. Our main technical tool is a higher-multiplicity version of the classical Whitney trick , by which pairs of isolated r -fold points of opposite sign can be eliminated by local modiffications of the map, assuming codimension d – dimK ≥ 3.\r\n\r\nAn important guiding idea for our work was that suffciency of the DPC, together with an old\r\nresult of Özaydin's on the existence of equivariant maps, might yield an approach to disproving the remaining open cases of the the long-standing topological Tverberg conjecture , i.e., to construct maps from the N -simplex σN to Rd without r-Tverberg points when r not a prime power and\r\nN = (d + 1)(r – 1). Unfortunately, our proof of the sufficiency of the DPC requires codimension d – dimK ≥ 3, which is not satisfied for K = σN .\r\n\r\nIn 2015, Frick [16] found a very elegant way to overcome this \\codimension 3 obstacle" and\r\nto construct the first counterexamples to the topological Tverberg conjecture for all parameters(d; r ) with d ≥ 3r + 1 and r not a prime power, by a reduction1 to a suitable lower-dimensional skeleton, for which the codimension 3 restriction is satisfied and maps without r -Tverberg points exist by Özaydin's result and sufficiency of the DPC.\r\n\r\nIn this thesis, we present a different construction (which does not use the constraint method) that yields counterexamples for d ≥ 3r , r not a prime power. ","lang":"eng"}],"month":"08","publisher":"IST Austria","department":[{"_id":"UlWa"}],"acknowledgement":"Foremost, I would like to thank Uli Wagner for introducing me to the exciting interface between\r\ntopology and combinatorics, and for our subsequent years of fruitful collaboration.\r\nIn our creative endeavors to eliminate intersection points, we had the chance to be joined later\r\nby Sergey Avvakumov and Arkadiy Skopenkov, which led us to new surprises in dimension 12.\r\nMy stay at EPFL and IST Austria was made very agreeable thanks to all these wonderful\r\npeople: Cyril Becker, Marek Filakovsky, Peter Franek, Radoslav Fulek, Peter Gazi, Kristof Huszar,\r\nMarek Krcal, Zuzana Masarova, Arnaud de Mesmay, Filip Moric, Michal Rybar, Martin Tancer,\r\nand Stephan Zhechev.\r\nFinally, I would like to thank my thesis committee Herbert Edelsbrunner and Roman Karasev\r\nfor their careful reading of the present manuscript and for the many improvements they suggested.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"}]