[{"title":"On the complexity of scrypt and proofs of space in the parallel random oracle model","author":[{"full_name":"Alwen, Joel F","last_name":"Alwen","id":"2A8DFA8C-F248-11E8-B48F-1D18A9856A87","first_name":"Joel F"},{"first_name":"Binyi","last_name":"Chen","full_name":"Chen, Binyi"},{"first_name":"Chethan","id":"4BD3F30E-F248-11E8-B48F-1D18A9856A87","full_name":"Kamath Hosdurg, Chethan","last_name":"Kamath Hosdurg"},{"first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov"},{"full_name":"Pietrzak, Krzysztof Z","orcid":"0000-0002-9139-1654","last_name":"Pietrzak","id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87","first_name":"Krzysztof Z"},{"full_name":"Tessaro, Stefano","last_name":"Tessaro","first_name":"Stefano"}],"publist_id":"6103","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"ieee":"J. F. Alwen, B. Chen, C. Kamath Hosdurg, V. Kolmogorov, K. Z. Pietrzak, and S. Tessaro, “On the complexity of scrypt and proofs of space in the parallel random oracle model,” presented at the EUROCRYPT: Theory and Applications of Cryptographic Techniques, Vienna, Austria, 2016, vol. 9666, pp. 358–387.","short":"J.F. Alwen, B. Chen, C. Kamath Hosdurg, V. Kolmogorov, K.Z. Pietrzak, S. Tessaro, in:, Springer, 2016, pp. 358–387.","ama":"Alwen JF, Chen B, Kamath Hosdurg C, Kolmogorov V, Pietrzak KZ, Tessaro S. On the complexity of scrypt and proofs of space in the parallel random oracle model. In: Vol 9666. Springer; 2016:358-387. doi:10.1007/978-3-662-49896-5_13","apa":"Alwen, J. F., Chen, B., Kamath Hosdurg, C., Kolmogorov, V., Pietrzak, K. Z., & Tessaro, S. (2016). On the complexity of scrypt and proofs of space in the parallel random oracle model (Vol. 9666, pp. 358–387). Presented at the EUROCRYPT: Theory and Applications of Cryptographic Techniques, Vienna, Austria: Springer. https://doi.org/10.1007/978-3-662-49896-5_13","mla":"Alwen, Joel F., et al. On the Complexity of Scrypt and Proofs of Space in the Parallel Random Oracle Model. Vol. 9666, Springer, 2016, pp. 358–87, doi:10.1007/978-3-662-49896-5_13.","ista":"Alwen JF, Chen B, Kamath Hosdurg C, Kolmogorov V, Pietrzak KZ, Tessaro S. 2016. On the complexity of scrypt and proofs of space in the parallel random oracle model. EUROCRYPT: Theory and Applications of Cryptographic Techniques, LNCS, vol. 9666, 358–387.","chicago":"Alwen, Joel F, Binyi Chen, Chethan Kamath Hosdurg, Vladimir Kolmogorov, Krzysztof Z Pietrzak, and Stefano Tessaro. “On the Complexity of Scrypt and Proofs of Space in the Parallel Random Oracle Model,” 9666:358–87. Springer, 2016. https://doi.org/10.1007/978-3-662-49896-5_13."},"project":[{"grant_number":"259668","name":"Provable Security for Physical Cryptography","call_identifier":"FP7","_id":"258C570E-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice"}],"date_published":"2016-04-28T00:00:00Z","doi":"10.1007/978-3-662-49896-5_13","date_created":"2018-12-11T11:50:51Z","page":"358 - 387","day":"28","year":"2016","publisher":"Springer","quality_controlled":"1","oa":1,"acknowledgement":"Joël Alwen, Chethan Kamath, and Krzysztof Pietrzak’s research is partially supported by an ERC starting grant (259668-PSPC). Vladimir Kolmogorov is partially supported by an ERC consolidator grant (616160-DOICV). Binyi Chen was partially supported by NSF grants CNS-1423566 and CNS-1514526, and a gift from the Gareatis Foundation. Stefano Tessaro was partially supported by NSF grants CNS-1423566, CNS-1528178, a Hellman Fellowship, and the Glen and Susanne Culler Chair.\r\n\r\nThis work was done in part while the authors were visiting the Simons Institute for the Theory of Computing, supported by the Simons Foundation and by the DIMACS/Simons Collaboration in Cryptography through NSF grant CNS-1523467.","department":[{"_id":"KrPi"},{"_id":"VlKo"}],"date_updated":"2021-01-12T06:49:15Z","status":"public","type":"conference","conference":{"name":"EUROCRYPT: Theory and Applications of Cryptographic Techniques","end_date":"2016-05-12","location":"Vienna, Austria","start_date":"2016-05-08"},"_id":"1231","volume":9666,"ec_funded":1,"language":[{"iso":"eng"}],"publication_status":"published","month":"04","intvolume":" 9666","alternative_title":["LNCS"],"scopus_import":1,"main_file_link":[{"open_access":"1","url":"https://eprint.iacr.org/2016/100"}],"oa_version":"Submitted Version","abstract":[{"text":"We study the time-and memory-complexities of the problem of computing labels of (multiple) randomly selected challenge-nodes in a directed acyclic graph. The w-bit label of a node is the hash of the labels of its parents, and the hash function is modeled as a random oracle. Specific instances of this problem underlie both proofs of space [Dziembowski et al. CRYPTO’15] as well as popular memory-hard functions like scrypt. As our main tool, we introduce the new notion of a probabilistic parallel entangled pebbling game, a new type of combinatorial pebbling game on a graph, which is closely related to the labeling game on the same graph. As a first application of our framework, we prove that for scrypt, when the underlying hash function is invoked n times, the cumulative memory complexity (CMC) (a notion recently introduced by Alwen and Serbinenko (STOC’15) to capture amortized memory-hardness for parallel adversaries) is at least Ω(w · (n/ log(n))2). This bound holds for adversaries that can store many natural functions of the labels (e.g., linear combinations), but still not arbitrary functions thereof. We then introduce and study a combinatorial quantity, and show how a sufficiently small upper bound on it (which we conjecture) extends our CMC bound for scrypt to hold against arbitrary adversaries. We also show that such an upper bound solves the main open problem for proofs-of-space protocols: namely, establishing that the time complexity of computing the label of a random node in a graph on n nodes (given an initial kw-bit state) reduces tightly to the time complexity for black pebbling on the same graph (given an initial k-node pebbling).","lang":"eng"}]},{"oa":1,"quality_controlled":"1","publisher":"World Scientific Publishing","acknowledgement":"Libor Barto and Alexandr Kazda were supported by the the Grant Agency of the Czech Republic, grant GACR 13-01832S. ","page":"1033 - 1060","date_created":"2018-12-11T11:51:32Z","doi":"10.1142/S0218196716500430","date_published":"2016-07-20T00:00:00Z","year":"2016","publication":"International Journal of Algebra and Computation","day":"20","author":[{"first_name":"Libor","last_name":"Barto","full_name":"Barto, Libor"},{"first_name":"Alexandr","id":"3B32BAA8-F248-11E8-B48F-1D18A9856A87","last_name":"Kazda","full_name":"Kazda, Alexandr"}],"publist_id":"5893","title":"Deciding absorption","citation":{"ista":"Barto L, Kazda A. 2016. Deciding absorption. International Journal of Algebra and Computation. 26(5), 1033–1060.","chicago":"Barto, Libor, and Alexandr Kazda. “Deciding Absorption.” International Journal of Algebra and Computation. World Scientific Publishing, 2016. https://doi.org/10.1142/S0218196716500430.","ama":"Barto L, Kazda A. Deciding absorption. International Journal of Algebra and Computation. 2016;26(5):1033-1060. doi:10.1142/S0218196716500430","apa":"Barto, L., & Kazda, A. (2016). Deciding absorption. International Journal of Algebra and Computation. World Scientific Publishing. https://doi.org/10.1142/S0218196716500430","ieee":"L. Barto and A. Kazda, “Deciding absorption,” International Journal of Algebra and Computation, vol. 26, no. 5. World Scientific Publishing, pp. 1033–1060, 2016.","short":"L. Barto, A. Kazda, International Journal of Algebra and Computation 26 (2016) 1033–1060.","mla":"Barto, Libor, and Alexandr Kazda. “Deciding Absorption.” International Journal of Algebra and Computation, vol. 26, no. 5, World Scientific Publishing, 2016, pp. 1033–60, doi:10.1142/S0218196716500430."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"url":"http://arxiv.org/abs/1512.07009","open_access":"1"}],"scopus_import":1,"intvolume":" 26","month":"07","abstract":[{"lang":"eng","text":"We characterize absorption in finite idempotent algebras by means of Jónsson absorption and cube term blockers. As an application we show that it is decidable whether a given subset is an absorbing subuniverse of an algebra given by the tables of its basic operations."}],"oa_version":"Preprint","issue":"5","volume":26,"publication_status":"published","language":[{"iso":"eng"}],"type":"journal_article","status":"public","_id":"1353","department":[{"_id":"VlKo"}],"date_updated":"2021-01-12T06:50:06Z"},{"month":"05","intvolume":" 9","scopus_import":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1502.07770"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"We consider the problem of minimizing the continuous valued total variation subject to different unary terms on trees and propose fast direct algorithms based on dynamic programming to solve these problems. We treat both the convex and the nonconvex case and derive worst-case complexities that are equal to or better than existing methods. We show applications to total variation based two dimensional image processing and computer vision problems based on a Lagrangian decomposition approach. The resulting algorithms are very effcient, offer a high degree of parallelism, and come along with memory requirements which are only in the order of the number of image pixels."}],"volume":9,"issue":"2","ec_funded":1,"language":[{"iso":"eng"}],"publication_status":"published","status":"public","type":"journal_article","_id":"1377","department":[{"_id":"VlKo"}],"date_updated":"2021-01-12T06:50:15Z","quality_controlled":"1","publisher":"Society for Industrial and Applied Mathematics ","oa":1,"doi":"10.1137/15M1010257","date_published":"2016-05-03T00:00:00Z","date_created":"2018-12-11T11:51:40Z","page":"605 - 636","day":"03","publication":"SIAM Journal on Imaging Sciences","year":"2016","project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"title":"Total variation on a tree","author":[{"last_name":"Kolmogorov","full_name":"Kolmogorov, Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","first_name":"Vladimir"},{"first_name":"Thomas","last_name":"Pock","full_name":"Pock, Thomas"},{"id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87","first_name":"Michal","last_name":"Rolinek","full_name":"Rolinek, Michal"}],"publist_id":"5834","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Kolmogorov, Vladimir, Thomas Pock, and Michal Rolinek. “Total Variation on a Tree.” SIAM Journal on Imaging Sciences. Society for Industrial and Applied Mathematics , 2016. https://doi.org/10.1137/15M1010257.","ista":"Kolmogorov V, Pock T, Rolinek M. 2016. Total variation on a tree. SIAM Journal on Imaging Sciences. 9(2), 605–636.","mla":"Kolmogorov, Vladimir, et al. “Total Variation on a Tree.” SIAM Journal on Imaging Sciences, vol. 9, no. 2, Society for Industrial and Applied Mathematics , 2016, pp. 605–36, doi:10.1137/15M1010257.","ama":"Kolmogorov V, Pock T, Rolinek M. Total variation on a tree. SIAM Journal on Imaging Sciences. 2016;9(2):605-636. doi:10.1137/15M1010257","apa":"Kolmogorov, V., Pock, T., & Rolinek, M. (2016). Total variation on a tree. SIAM Journal on Imaging Sciences. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/15M1010257","ieee":"V. Kolmogorov, T. Pock, and M. Rolinek, “Total variation on a tree,” SIAM Journal on Imaging Sciences, vol. 9, no. 2. Society for Industrial and Applied Mathematics , pp. 605–636, 2016.","short":"V. Kolmogorov, T. Pock, M. Rolinek, SIAM Journal on Imaging Sciences 9 (2016) 605–636."}},{"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Kazda, Alexandr. “CSP for Binary Conservative Relational Structures.” Algebra Universalis. Springer, 2016. https://doi.org/10.1007/s00012-015-0358-8.","ista":"Kazda A. 2016. CSP for binary conservative relational structures. Algebra Universalis. 75(1), 75–84.","mla":"Kazda, Alexandr. “CSP for Binary Conservative Relational Structures.” Algebra Universalis, vol. 75, no. 1, Springer, 2016, pp. 75–84, doi:10.1007/s00012-015-0358-8.","short":"A. Kazda, Algebra Universalis 75 (2016) 75–84.","ieee":"A. Kazda, “CSP for binary conservative relational structures,” Algebra Universalis, vol. 75, no. 1. Springer, pp. 75–84, 2016.","apa":"Kazda, A. (2016). CSP for binary conservative relational structures. Algebra Universalis. Springer. https://doi.org/10.1007/s00012-015-0358-8","ama":"Kazda A. CSP for binary conservative relational structures. Algebra Universalis. 2016;75(1):75-84. doi:10.1007/s00012-015-0358-8"},"date_updated":"2021-01-12T06:52:00Z","title":"CSP for binary conservative relational structures","department":[{"_id":"VlKo"}],"publist_id":"5554","author":[{"id":"3B32BAA8-F248-11E8-B48F-1D18A9856A87","first_name":"Alexandr","last_name":"Kazda","full_name":"Kazda, Alexandr"}],"_id":"1612","status":"public","type":"journal_article","publication":"Algebra Universalis","language":[{"iso":"eng"}],"day":"01","year":"2016","publication_status":"published","date_created":"2018-12-11T11:53:01Z","issue":"1","volume":75,"date_published":"2016-02-01T00:00:00Z","doi":"10.1007/s00012-015-0358-8","page":"75 - 84","oa_version":"Preprint","abstract":[{"text":"We prove that whenever A is a 3-conservative relational structure with only binary and unary relations,then the algebra of polymorphisms of A either has no Taylor operation (i.e.,CSP(A)is NP-complete),or it generates an SD(∧) variety (i.e.,CSP(A)has bounded width).","lang":"eng"}],"intvolume":" 75","month":"02","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1112.1099"}],"oa":1,"publisher":"Springer","quality_controlled":"1","scopus_import":1},{"related_material":{"record":[{"relation":"later_version","id":"5975","status":"public"}]},"volume":"2016-December","ec_funded":1,"language":[{"iso":"eng"}],"publication_status":"published","month":"12","scopus_import":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1506.08547v7"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"We consider the recent formulation of the Algorithmic Lovász Local Lemma [1], [2] for finding objects that avoid "bad features", or "flaws". It extends the Moser-Tardos resampling algorithm [3] to more general discrete spaces. At each step the method picks a flaw present in the current state and "resamples" it using a "resampling oracle" provided by the user. However, it is less flexible than the Moser-Tardos method since [1], [2] require a specific flaw selection rule, whereas [3] allows an arbitrary rule (and thus can potentially be implemented more efficiently). We formulate a new "commutativity" condition, and prove that it is sufficient for an arbitrary rule to work. It also enables an efficient parallelization under an additional assumption. We then show that existing resampling oracles for perfect matchings and permutations do satisfy this condition. Finally, we generalize the precondition in [2] (in the case of symmetric potential causality graphs). This unifies special cases that previously were treated separately."}],"department":[{"_id":"VlKo"}],"date_updated":"2023-09-19T14:24:57Z","status":"public","type":"conference","conference":{"name":"FOCS: Foundations of Computer Science","location":"New Brunswick, NJ, USA ","end_date":"2016-09-11","start_date":"2016-09-09"},"_id":"1193","doi":"10.1109/FOCS.2016.88","date_published":"2016-12-15T00:00:00Z","date_created":"2018-12-11T11:50:38Z","day":"15","publication":"Proceedings - Annual IEEE Symposium on Foundations of Computer Science","year":"2016","publisher":"IEEE","quality_controlled":"1","oa":1,"acknowledgement":"European Unions Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no 616160","title":"Commutativity in the algorithmic Lovasz local lemma","publist_id":"6158","author":[{"last_name":"Kolmogorov","full_name":"Kolmogorov, Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","first_name":"Vladimir"}],"article_processing_charge":"No","external_id":{"arxiv":["1506.08547"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Kolmogorov, Vladimir. “Commutativity in the Algorithmic Lovasz Local Lemma.” In Proceedings - Annual IEEE Symposium on Foundations of Computer Science, Vol. 2016–December. IEEE, 2016. https://doi.org/10.1109/FOCS.2016.88.","ista":"Kolmogorov V. 2016. Commutativity in the algorithmic Lovasz local lemma. Proceedings - Annual IEEE Symposium on Foundations of Computer Science. FOCS: Foundations of Computer Science vol. 2016–December, 7782993.","mla":"Kolmogorov, Vladimir. “Commutativity in the Algorithmic Lovasz Local Lemma.” Proceedings - Annual IEEE Symposium on Foundations of Computer Science, vol. 2016–December, 7782993, IEEE, 2016, doi:10.1109/FOCS.2016.88.","apa":"Kolmogorov, V. (2016). Commutativity in the algorithmic Lovasz local lemma. In Proceedings - Annual IEEE Symposium on Foundations of Computer Science (Vol. 2016–December). New Brunswick, NJ, USA : IEEE. https://doi.org/10.1109/FOCS.2016.88","ama":"Kolmogorov V. Commutativity in the algorithmic Lovasz local lemma. In: Proceedings - Annual IEEE Symposium on Foundations of Computer Science. Vol 2016-December. IEEE; 2016. doi:10.1109/FOCS.2016.88","short":"V. Kolmogorov, in:, Proceedings - Annual IEEE Symposium on Foundations of Computer Science, IEEE, 2016.","ieee":"V. Kolmogorov, “Commutativity in the algorithmic Lovasz local lemma,” in Proceedings - Annual IEEE Symposium on Foundations of Computer Science, New Brunswick, NJ, USA , 2016, vol. 2016–December."},"project":[{"grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice","_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"article_number":"7782993"},{"main_file_link":[{"url":"http://arxiv.org/abs/1210.0508","open_access":"1"}],"scopus_import":1,"intvolume":" 76","month":"09","abstract":[{"text":"We consider Conditional random fields (CRFs) with pattern-based potentials defined on a chain. In this model the energy of a string (labeling) (Formula presented.) is the sum of terms over intervals [i, j] where each term is non-zero only if the substring (Formula presented.) equals a prespecified pattern w. Such CRFs can be naturally applied to many sequence tagging problems. We present efficient algorithms for the three standard inference tasks in a CRF, namely computing (i) the partition function, (ii) marginals, and (iii) computing the MAP. Their complexities are respectively (Formula presented.), (Formula presented.) and (Formula presented.) where L is the combined length of input patterns, (Formula presented.) is the maximum length of a pattern, and D is the input alphabet. This improves on the previous algorithms of Ye et al. (NIPS, 2009) whose complexities are respectively (Formula presented.), (Formula presented.) and (Formula presented.), where (Formula presented.) is the number of input patterns. In addition, we give an efficient algorithm for sampling, and revisit the case of MAP with non-positive weights.","lang":"eng"}],"oa_version":"Preprint","ec_funded":1,"volume":76,"issue":"1","related_material":{"record":[{"id":"2272","status":"public","relation":"earlier_version"}]},"publication_status":"published","language":[{"iso":"eng"}],"type":"journal_article","status":"public","_id":"1794","department":[{"_id":"VlKo"}],"date_updated":"2023-10-17T09:51:31Z","oa":1,"publisher":"Springer","quality_controlled":"1","acknowledgement":"This work has been partially supported by the European Research Council under the European Unions Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no. 616160.","page":"17 - 46","date_created":"2018-12-11T11:54:02Z","date_published":"2016-09-01T00:00:00Z","doi":"10.1007/s00453-015-0017-7","year":"2016","publication":"Algorithmica","day":"01","project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"external_id":{"arxiv":["1210.0508"]},"publist_id":"5316","author":[{"first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","last_name":"Kolmogorov","full_name":"Kolmogorov, Vladimir"},{"id":"2CCAC26C-F248-11E8-B48F-1D18A9856A87","first_name":"Rustem","full_name":"Takhanov, Rustem","last_name":"Takhanov"}],"title":"Inference algorithms for pattern-based CRFs on sequence data","citation":{"ieee":"V. Kolmogorov and R. Takhanov, “Inference algorithms for pattern-based CRFs on sequence data,” Algorithmica, vol. 76, no. 1. Springer, pp. 17–46, 2016.","short":"V. Kolmogorov, R. Takhanov, Algorithmica 76 (2016) 17–46.","apa":"Kolmogorov, V., & Takhanov, R. (2016). Inference algorithms for pattern-based CRFs on sequence data. Algorithmica. Springer. https://doi.org/10.1007/s00453-015-0017-7","ama":"Kolmogorov V, Takhanov R. Inference algorithms for pattern-based CRFs on sequence data. Algorithmica. 2016;76(1):17-46. doi:10.1007/s00453-015-0017-7","mla":"Kolmogorov, Vladimir, and Rustem Takhanov. “Inference Algorithms for Pattern-Based CRFs on Sequence Data.” Algorithmica, vol. 76, no. 1, Springer, 2016, pp. 17–46, doi:10.1007/s00453-015-0017-7.","ista":"Kolmogorov V, Takhanov R. 2016. Inference algorithms for pattern-based CRFs on sequence data. Algorithmica. 76(1), 17–46.","chicago":"Kolmogorov, Vladimir, and Rustem Takhanov. “Inference Algorithms for Pattern-Based CRFs on Sequence Data.” Algorithmica. 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Synthetic discrete tomography problems, Institute of Science and Technology Austria, 10.15479/AT:ISTA:46.","mla":"Swoboda, Paul. Synthetic Discrete Tomography Problems. Institute of Science and Technology Austria, 2016, doi:10.15479/AT:ISTA:46.","ieee":"P. Swoboda, “Synthetic discrete tomography problems.” Institute of Science and Technology Austria, 2016.","short":"P. Swoboda, (2016).","apa":"Swoboda, P. (2016). Synthetic discrete tomography problems. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:46","ama":"Swoboda P. Synthetic discrete tomography problems. 2016. doi:10.15479/AT:ISTA:46"},"department":[{"_id":"VlKo"}],"title":"Synthetic discrete tomography problems","file_date_updated":"2020-07-14T12:47:02Z","article_processing_charge":"No","author":[{"id":"446560C6-F248-11E8-B48F-1D18A9856A87","first_name":"Paul","last_name":"Swoboda","full_name":"Swoboda, Paul"}],"_id":"5557","keyword":["discrete tomography"],"status":"public","tmp":{"image":"/images/cc_0.png","legal_code_url":"https://creativecommons.org/publicdomain/zero/1.0/legalcode","name":"Creative Commons Public Domain Dedication (CC0 1.0)","short":"CC0 (1.0)"},"type":"research_data"},{"page":"566 - 577","date_created":"2018-12-11T11:53:10Z","date_published":"2015-12-01T00:00:00Z","doi":"10.1007/978-3-662-48971-0_48","year":"2015","publication":"26th International Symposium","day":"01","oa":1,"quality_controlled":"1","publisher":"Springer Nature","article_processing_charge":"No","external_id":{"arxiv":["1504.07067"]},"publist_id":"5519","author":[{"first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov"},{"full_name":"Rolinek, Michal","last_name":"Rolinek","first_name":"Michal","id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Takhanov, Rustem","last_name":"Takhanov","first_name":"Rustem"}],"title":"Effectiveness of structural restrictions for hybrid CSPs","citation":{"mla":"Kolmogorov, Vladimir, et al. “Effectiveness of Structural Restrictions for Hybrid CSPs.” 26th International Symposium, vol. 9472, Springer Nature, 2015, pp. 566–77, doi:10.1007/978-3-662-48971-0_48.","ieee":"V. Kolmogorov, M. Rolinek, and R. Takhanov, “Effectiveness of structural restrictions for hybrid CSPs,” in 26th International Symposium, Nagoya, Japan, 2015, vol. 9472, pp. 566–577.","short":"V. Kolmogorov, M. Rolinek, R. Takhanov, in:, 26th International Symposium, Springer Nature, 2015, pp. 566–577.","apa":"Kolmogorov, V., Rolinek, M., & Takhanov, R. (2015). Effectiveness of structural restrictions for hybrid CSPs. In 26th International Symposium (Vol. 9472, pp. 566–577). Nagoya, Japan: Springer Nature. https://doi.org/10.1007/978-3-662-48971-0_48","ama":"Kolmogorov V, Rolinek M, Takhanov R. Effectiveness of structural restrictions for hybrid CSPs. In: 26th International Symposium. Vol 9472. Springer Nature; 2015:566-577. doi:10.1007/978-3-662-48971-0_48","chicago":"Kolmogorov, Vladimir, Michal Rolinek, and Rustem Takhanov. “Effectiveness of Structural Restrictions for Hybrid CSPs.” In 26th International Symposium, 9472:566–77. Springer Nature, 2015. https://doi.org/10.1007/978-3-662-48971-0_48.","ista":"Kolmogorov V, Rolinek M, Takhanov R. 2015. Effectiveness of structural restrictions for hybrid CSPs. 26th International Symposium. ISAAC: International Symposium on Algorithms and Computation, LNCS, vol. 9472, 566–577."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"ec_funded":1,"volume":9472,"publication_status":"published","publication_identifier":{"isbn":["978-3-662-48970-3"]},"language":[{"iso":"eng"}],"main_file_link":[{"url":"http://arxiv.org/abs/1504.07067","open_access":"1"}],"scopus_import":"1","alternative_title":["LNCS"],"intvolume":" 9472","month":"12","abstract":[{"lang":"eng","text":"Constraint Satisfaction Problem (CSP) is a fundamental algorithmic problem that appears in many areas of Computer Science. It can be equivalently stated as computing a homomorphism R→ΓΓ between two relational structures, e.g. between two directed graphs. Analyzing its complexity has been a prominent research direction, especially for the fixed template CSPs where the right side ΓΓ is fixed and the left side R is unconstrained.\r\n\r\nFar fewer results are known for the hybrid setting that restricts both sides simultaneously. It assumes that R belongs to a certain class of relational structures (called a structural restriction in this paper). We study which structural restrictions are effective, i.e. there exists a fixed template ΓΓ (from a certain class of languages) for which the problem is tractable when R is restricted, and NP-hard otherwise. We provide a characterization for structural restrictions that are closed under inverse homomorphisms. The criterion is based on the chromatic number of a relational structure defined in this paper; it generalizes the standard chromatic number of a graph.\r\n\r\nAs our main tool, we use the algebraic machinery developed for fixed template CSPs. To apply it to our case, we introduce a new construction called a “lifted language”. We also give a characterization for structural restrictions corresponding to minor-closed families of graphs, extend results to certain Valued CSPs (namely conservative valued languages), and state implications for (valued) CSPs with ordered variables and for the maximum weight independent set problem on some restricted families of graphs."}],"oa_version":"Preprint","department":[{"_id":"VlKo"}],"date_updated":"2022-02-01T15:12:35Z","conference":{"start_date":"2015-12-09","end_date":"2015-12-11","location":"Nagoya, Japan","name":"ISAAC: International Symposium on Algorithms and Computation"},"type":"conference","status":"public","_id":"1636"},{"date_updated":"2021-01-12T06:53:33Z","department":[{"_id":"VlKo"}],"_id":"1841","status":"public","type":"journal_article","language":[{"iso":"eng"}],"publication_status":"published","issue":"5","volume":37,"ec_funded":1,"oa_version":"Preprint","abstract":[{"lang":"eng","text":"We propose a new family of message passing techniques for MAP estimation in graphical models which we call Sequential Reweighted Message Passing (SRMP). Special cases include well-known techniques such as Min-Sum Diffusion (MSD) and a faster Sequential Tree-Reweighted Message Passing (TRW-S). Importantly, our derivation is simpler than the original derivation of TRW-S, and does not involve a decomposition into trees. This allows easy generalizations. The new family of algorithms can be viewed as a generalization of TRW-S from pairwise to higher-order graphical models. We test SRMP on several real-world problems with promising results."}],"month":"05","intvolume":" 37","scopus_import":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1309.5655"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ama":"Kolmogorov V. A new look at reweighted message passing. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2015;37(5):919-930. doi:10.1109/TPAMI.2014.2363465","apa":"Kolmogorov, V. (2015). A new look at reweighted message passing. IEEE Transactions on Pattern Analysis and Machine Intelligence. IEEE. https://doi.org/10.1109/TPAMI.2014.2363465","ieee":"V. Kolmogorov, “A new look at reweighted message passing,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 37, no. 5. IEEE, pp. 919–930, 2015.","short":"V. Kolmogorov, IEEE Transactions on Pattern Analysis and Machine Intelligence 37 (2015) 919–930.","mla":"Kolmogorov, Vladimir. “A New Look at Reweighted Message Passing.” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 37, no. 5, IEEE, 2015, pp. 919–30, doi:10.1109/TPAMI.2014.2363465.","ista":"Kolmogorov V. 2015. A new look at reweighted message passing. IEEE Transactions on Pattern Analysis and Machine Intelligence. 37(5), 919–930.","chicago":"Kolmogorov, Vladimir. “A New Look at Reweighted Message Passing.” IEEE Transactions on Pattern Analysis and Machine Intelligence. IEEE, 2015. https://doi.org/10.1109/TPAMI.2014.2363465."},"title":"A new look at reweighted message passing","publist_id":"5261","author":[{"id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","first_name":"Vladimir","full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov"}],"project":[{"call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425","grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice"}],"day":"01","publication":"IEEE Transactions on Pattern Analysis and Machine Intelligence","year":"2015","date_published":"2015-05-01T00:00:00Z","doi":"10.1109/TPAMI.2014.2363465","date_created":"2018-12-11T11:54:18Z","page":"919 - 930","publisher":"IEEE","quality_controlled":"1","oa":1},{"ec_funded":1,"date_created":"2018-12-11T11:54:24Z","date_published":"2015-06-01T00:00:00Z","doi":"10.1109/CVPR.2015.7298890","page":"2737 - 2745","language":[{"iso":"eng"}],"day":"01","publication_status":"published","year":"2015","month":"06","oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1408.6804"}],"scopus_import":1,"publisher":"IEEE","quality_controlled":"1","oa_version":"Preprint","abstract":[{"text":"Structural support vector machines (SSVMs) are amongst the best performing models for structured computer vision tasks, such as semantic image segmentation or human pose estimation. Training SSVMs, however, is computationally costly, because it requires repeated calls to a structured prediction subroutine (called \\emph{max-oracle}), which has to solve an optimization problem itself, e.g. a graph cut.\r\nIn this work, we introduce a new algorithm for SSVM training that is more efficient than earlier techniques when the max-oracle is computationally expensive, as it is frequently the case in computer vision tasks. The main idea is to (i) combine the recent stochastic Block-Coordinate Frank-Wolfe algorithm with efficient hyperplane caching, and (ii) use an automatic selection rule for deciding whether to call the exact max-oracle or to rely on an approximate one based on the cached hyperplanes.\r\nWe show experimentally that this strategy leads to faster convergence to the optimum with respect to the number of requires oracle calls, and that this translates into faster convergence with respect to the total runtime when the max-oracle is slow compared to the other steps of the algorithm. ","lang":"eng"}],"department":[{"_id":"VlKo"},{"_id":"ChLa"}],"title":"A multi-plane block-coordinate Frank-Wolfe algorithm for training structural SVMs with a costly max-oracle","author":[{"first_name":"Neel","id":"31ABAF80-F248-11E8-B48F-1D18A9856A87","last_name":"Shah","full_name":"Shah, Neel"},{"last_name":"Kolmogorov","full_name":"Kolmogorov, Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","first_name":"Vladimir"},{"last_name":"Lampert","full_name":"Lampert, Christoph","orcid":"0000-0001-8622-7887","id":"40C20FD2-F248-11E8-B48F-1D18A9856A87","first_name":"Christoph"}],"publist_id":"5240","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T06:53:40Z","citation":{"ista":"Shah N, Kolmogorov V, Lampert C. 2015. A multi-plane block-coordinate Frank-Wolfe algorithm for training structural SVMs with a costly max-oracle. CVPR: Computer Vision and Pattern Recognition, 2737–2745.","chicago":"Shah, Neel, Vladimir Kolmogorov, and Christoph Lampert. “A Multi-Plane Block-Coordinate Frank-Wolfe Algorithm for Training Structural SVMs with a Costly Max-Oracle,” 2737–45. IEEE, 2015. https://doi.org/10.1109/CVPR.2015.7298890.","apa":"Shah, N., Kolmogorov, V., & Lampert, C. (2015). A multi-plane block-coordinate Frank-Wolfe algorithm for training structural SVMs with a costly max-oracle (pp. 2737–2745). Presented at the CVPR: Computer Vision and Pattern Recognition, Boston, MA, USA: IEEE. https://doi.org/10.1109/CVPR.2015.7298890","ama":"Shah N, Kolmogorov V, Lampert C. A multi-plane block-coordinate Frank-Wolfe algorithm for training structural SVMs with a costly max-oracle. In: IEEE; 2015:2737-2745. doi:10.1109/CVPR.2015.7298890","short":"N. Shah, V. Kolmogorov, C. Lampert, in:, IEEE, 2015, pp. 2737–2745.","ieee":"N. Shah, V. Kolmogorov, and C. Lampert, “A multi-plane block-coordinate Frank-Wolfe algorithm for training structural SVMs with a costly max-oracle,” presented at the CVPR: Computer Vision and Pattern Recognition, Boston, MA, USA, 2015, pp. 2737–2745.","mla":"Shah, Neel, et al. A Multi-Plane Block-Coordinate Frank-Wolfe Algorithm for Training Structural SVMs with a Costly Max-Oracle. IEEE, 2015, pp. 2737–45, doi:10.1109/CVPR.2015.7298890."},"project":[{"grant_number":"308036","name":"Lifelong Learning of Visual Scene Understanding","_id":"2532554C-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice","_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"status":"public","conference":{"start_date":"2015-06-07","location":"Boston, MA, USA","end_date":"2015-06-12","name":"CVPR: Computer Vision and Pattern Recognition"},"type":"conference","_id":"1859"},{"month":"02","intvolume":" 44","scopus_import":1,"main_file_link":[{"url":"http://arxiv.org/abs/1311.4219","open_access":"1"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"A class of valued constraint satisfaction problems (VCSPs) is characterised by a valued constraint language, a fixed set of cost functions on a finite domain. Finite-valued constraint languages contain functions that take on rational costs and general-valued constraint languages contain functions that take on rational or infinite costs. An instance of the problem is specified by a sum of functions from the language with the goal to minimise the sum. This framework includes and generalises well-studied constraint satisfaction problems (CSPs) and maximum constraint satisfaction problems (Max-CSPs).\r\nOur main result is a precise algebraic characterisation of valued constraint languages whose instances can be solved exactly by the basic linear programming relaxation (BLP). For a general-valued constraint language Γ, BLP is a decision procedure for Γ if and only if Γ admits a symmetric fractional polymorphism of every arity. For a finite-valued constraint language Γ, BLP is a decision procedure if and only if Γ admits a symmetric fractional polymorphism of some arity, or equivalently, if Γ admits a symmetric fractional polymorphism of arity 2.\r\nUsing these results, we obtain tractability of several novel and previously widely-open classes of VCSPs, including problems over valued constraint languages that are: (1) submodular on arbitrary lattices; (2) bisubmodular (also known as k-submodular) on arbitrary finite domains; (3) weakly (and hence strongly) tree-submodular on arbitrary trees. "}],"issue":"1","volume":44,"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"2518"}]},"language":[{"iso":"eng"}],"publication_status":"published","status":"public","type":"journal_article","_id":"2271","department":[{"_id":"VlKo"}],"date_updated":"2023-02-23T10:46:30Z","publisher":"SIAM","quality_controlled":"1","oa":1,"date_published":"2015-02-01T00:00:00Z","doi":"10.1137/130945648","date_created":"2018-12-11T11:56:41Z","page":"1 - 36","day":"01","publication":"SIAM Journal on Computing","year":"2015","title":"The power of linear programming for general-valued CSPs","publist_id":"4673","author":[{"first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov"},{"last_name":"Thapper","full_name":"Thapper, Johan","first_name":"Johan"},{"full_name":"Živný, Stanislav","last_name":"Živný","first_name":"Stanislav"}],"external_id":{"arxiv":["1311.4219"]},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Kolmogorov V, Thapper J, Živný S. 2015. The power of linear programming for general-valued CSPs. SIAM Journal on Computing. 44(1), 1–36.","chicago":"Kolmogorov, Vladimir, Johan Thapper, and Stanislav Živný. “The Power of Linear Programming for General-Valued CSPs.” SIAM Journal on Computing. SIAM, 2015. https://doi.org/10.1137/130945648.","ama":"Kolmogorov V, Thapper J, Živný S. The power of linear programming for general-valued CSPs. SIAM Journal on Computing. 2015;44(1):1-36. doi:10.1137/130945648","apa":"Kolmogorov, V., Thapper, J., & Živný, S. (2015). The power of linear programming for general-valued CSPs. SIAM Journal on Computing. SIAM. https://doi.org/10.1137/130945648","short":"V. Kolmogorov, J. Thapper, S. Živný, SIAM Journal on Computing 44 (2015) 1–36.","ieee":"V. Kolmogorov, J. Thapper, and S. Živný, “The power of linear programming for general-valued CSPs,” SIAM Journal on Computing, vol. 44, no. 1. SIAM, pp. 1–36, 2015.","mla":"Kolmogorov, Vladimir, et al. “The Power of Linear Programming for General-Valued CSPs.” SIAM Journal on Computing, vol. 44, no. 1, SIAM, 2015, pp. 1–36, doi:10.1137/130945648."}},{"citation":{"ama":"Kolmogorov V, Krokhin A, Rolinek M. The complexity of general-valued CSPs. In: IEEE; 2015:1246-1258. doi:10.1109/FOCS.2015.80","apa":"Kolmogorov, V., Krokhin, A., & Rolinek, M. (2015). The complexity of general-valued CSPs (pp. 1246–1258). Presented at the FOCS: Foundations of Computer Science, Berkeley, CA, United States: IEEE. https://doi.org/10.1109/FOCS.2015.80","ieee":"V. Kolmogorov, A. Krokhin, and M. Rolinek, “The complexity of general-valued CSPs,” presented at the FOCS: Foundations of Computer Science, Berkeley, CA, United States, 2015, pp. 1246–1258.","short":"V. Kolmogorov, A. Krokhin, M. Rolinek, in:, IEEE, 2015, pp. 1246–1258.","mla":"Kolmogorov, Vladimir, et al. The Complexity of General-Valued CSPs. IEEE, 2015, pp. 1246–58, doi:10.1109/FOCS.2015.80.","ista":"Kolmogorov V, Krokhin A, Rolinek M. 2015. The complexity of general-valued CSPs. FOCS: Foundations of Computer Science, 56th Annual Symposium on Foundations of Computer Science, , 1246–1258.","chicago":"Kolmogorov, Vladimir, Andrei Krokhin, and Michal Rolinek. “The Complexity of General-Valued CSPs,” 1246–58. IEEE, 2015. https://doi.org/10.1109/FOCS.2015.80."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","first_name":"Vladimir","full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov"},{"last_name":"Krokhin","full_name":"Krokhin, Andrei","first_name":"Andrei"},{"first_name":"Michal","id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87","full_name":"Rolinek, Michal","last_name":"Rolinek"}],"publist_id":"5518","title":"The complexity of general-valued CSPs","project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160","call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425"}],"year":"2015","day":"01","page":"1246 - 1258","date_created":"2018-12-11T11:53:10Z","date_published":"2015-12-01T00:00:00Z","doi":"10.1109/FOCS.2015.80","oa":1,"publisher":"IEEE","quality_controlled":"1","date_updated":"2023-02-23T12:44:26Z","department":[{"_id":"VlKo"}],"_id":"1637","conference":{"name":"FOCS: Foundations of Computer Science","location":"Berkeley, CA, United States","end_date":"2015-10-20","start_date":"2015-10-18"},"type":"conference","status":"public","publication_status":"published","language":[{"iso":"eng"}],"ec_funded":1,"related_material":{"record":[{"relation":"other","status":"public","id":"644"}]},"abstract":[{"lang":"eng","text":"An instance of the Valued Constraint Satisfaction Problem (VCSP) is given by a finite set of variables, a finite domain of labels, and a sum of functions, each function depending on a subset of the variables. Each function can take finite values specifying costs of assignments of labels to its variables or the infinite value, which indicates an infeasible assignment. The goal is to find an assignment of labels to the variables that minimizes the sum. We study, assuming that P ≠ NP, how the complexity of this very general problem depends on the set of functions allowed in the instances, the so-called constraint language. The case when all allowed functions take values in {0, ∞} corresponds to ordinary CSPs, where one deals only with the feasibility issue and there is no optimization. This case is the subject of the Algebraic CSP Dichotomy Conjecture predicting for which constraint languages CSPs are tractable (i.e. solvable in polynomial time) and for which NP-hard. The case when all allowed functions take only finite values corresponds to finite-valued CSP, where the feasibility aspect is trivial and one deals only with the optimization issue. The complexity of finite-valued CSPs was fully classified by Thapper and Zivny. An algebraic necessary condition for tractability of a general-valued CSP with a fixed constraint language was recently given by Kozik and Ochremiak. As our main result, we prove that if a constraint language satisfies this algebraic necessary condition, and the feasibility CSP (i.e. the problem of deciding whether a given instance has a feasible solution) corresponding to the VCSP with this language is tractable, then the VCSP is tractable. The algorithm is a simple combination of the assumed algorithm for the feasibility CSP and the standard LP relaxation. As a corollary, we obtain that a dichotomy for ordinary CSPs would imply a dichotomy for general-valued CSPs."}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1502.07327"}],"alternative_title":["56th Annual Symposium on Foundations of Computer Science"],"scopus_import":1,"month":"12"},{"page":"585 - 605","date_created":"2018-12-11T11:53:24Z","date_published":"2015-08-01T00:00:00Z","doi":"10.1007/978-3-662-48000-7_29","year":"2015","publication":"35th Annual Cryptology Conference","day":"01","oa":1,"quality_controlled":"1","publisher":"Springer","article_processing_charge":"No","author":[{"last_name":"Dziembowski","full_name":"Dziembowski, Stefan","first_name":"Stefan"},{"first_name":"Sebastian","last_name":"Faust","full_name":"Faust, Sebastian"},{"id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","first_name":"Vladimir","last_name":"Kolmogorov","full_name":"Kolmogorov, Vladimir"},{"full_name":"Pietrzak, Krzysztof Z","orcid":"0000-0002-9139-1654","last_name":"Pietrzak","first_name":"Krzysztof Z","id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"5474","title":"Proofs of space","citation":{"ista":"Dziembowski S, Faust S, Kolmogorov V, Pietrzak KZ. 2015. Proofs of space. 35th Annual Cryptology Conference. CRYPTO: International Cryptology Conference, LNCS, vol. 9216, 585–605.","chicago":"Dziembowski, Stefan, Sebastian Faust, Vladimir Kolmogorov, and Krzysztof Z Pietrzak. “Proofs of Space.” In 35th Annual Cryptology Conference, 9216:585–605. Springer, 2015. https://doi.org/10.1007/978-3-662-48000-7_29.","apa":"Dziembowski, S., Faust, S., Kolmogorov, V., & Pietrzak, K. Z. (2015). Proofs of space. In 35th Annual Cryptology Conference (Vol. 9216, pp. 585–605). Santa Barbara, CA, United States: Springer. https://doi.org/10.1007/978-3-662-48000-7_29","ama":"Dziembowski S, Faust S, Kolmogorov V, Pietrzak KZ. Proofs of space. In: 35th Annual Cryptology Conference. Vol 9216. Springer; 2015:585-605. doi:10.1007/978-3-662-48000-7_29","short":"S. Dziembowski, S. Faust, V. Kolmogorov, K.Z. Pietrzak, in:, 35th Annual Cryptology Conference, Springer, 2015, pp. 585–605.","ieee":"S. Dziembowski, S. Faust, V. Kolmogorov, and K. Z. Pietrzak, “Proofs of space,” in 35th Annual Cryptology Conference, Santa Barbara, CA, United States, 2015, vol. 9216, pp. 585–605.","mla":"Dziembowski, Stefan, et al. “Proofs of Space.” 35th Annual Cryptology Conference, vol. 9216, Springer, 2015, pp. 585–605, doi:10.1007/978-3-662-48000-7_29."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice","_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"name":"Provable Security for Physical Cryptography","grant_number":"259668","_id":"258C570E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"ec_funded":1,"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"2274"}]},"volume":9216,"publication_status":"published","publication_identifier":{"issn":["0302-9743"],"isbn":["9783662479995"]},"language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://eprint.iacr.org/2013/796.pdf"}],"scopus_import":"1","alternative_title":["LNCS"],"intvolume":" 9216","month":"08","abstract":[{"lang":"eng","text":"Proofs of work (PoW) have been suggested by Dwork and Naor (Crypto’92) as protection to a shared resource. The basic idea is to ask the service requestor to dedicate some non-trivial amount of computational work to every request. The original applications included prevention of spam and protection against denial of service attacks. More recently, PoWs have been used to prevent double spending in the Bitcoin digital currency system. In this work, we put forward an alternative concept for PoWs - so-called proofs of space (PoS), where a service requestor must dedicate a significant amount of disk space as opposed to computation. We construct secure PoS schemes in the random oracle model (with one additional mild assumption required for the proof to go through), using graphs with high “pebbling complexity” and Merkle hash-trees. We discuss some applications, including follow-up work where a decentralized digital currency scheme called Spacecoin is constructed that uses PoS (instead of wasteful PoW like in Bitcoin) to prevent double spending. The main technical contribution of this work is the construction of (directed, loop-free) graphs on N vertices with in-degree O(log logN) such that even if one places Θ(N) pebbles on the nodes of the graph, there’s a constant fraction of nodes that needs Θ(N) steps to be pebbled (where in every step one can put a pebble on a node if all its parents have a pebble)."}],"oa_version":"Preprint","department":[{"_id":"VlKo"},{"_id":"KrPi"}],"date_updated":"2024-03-20T08:31:49Z","conference":{"name":"CRYPTO: International Cryptology Conference","end_date":"2015-08-20","location":"Santa Barbara, CA, United States","start_date":"2015-08-16"},"type":"conference","pubrep_id":"671","status":"public","_id":"1675"},{"oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"Energies with high-order non-submodular interactions have been shown to be very useful in vision due to their high modeling power. Optimization of such energies, however, is generally NP-hard. A naive approach that works for small problem instances is exhaustive search, that is, enumeration of all possible labelings of the underlying graph. We propose a general minimization approach for large graphs based on enumeration of labelings of certain small patches. \r\nThis partial enumeration technique reduces complex high-order energy formulations to pairwise Constraint Satisfaction Problems with unary costs (uCSP), which can be efficiently solved using standard methods like TRW-S. Our approach outperforms a number of existing state-of-the-art algorithms on well known difficult problems (e.g. curvature regularization, stereo, deconvolution); it gives near global minimum and better speed. \r\nOur main application of interest is curvature regularization. In the context of segmentation, our partial enumeration technique allows to evaluate curvature directly on small patches using a novel integral geometry approach.\r\n"}],"month":"03","scopus_import":1,"file":[{"file_id":"4754","checksum":"4a74b5c92d6dcd2348c2c10ec8dd18bf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2018-12-12T10:09:30Z","file_name":"IST-2016-566-v1+1_iccv13_part_enumeration.pdf","date_updated":"2020-07-14T12:45:36Z","file_size":378601,"creator":"system"}],"language":[{"iso":"eng"}],"publication_status":"published","_id":"2275","status":"public","pubrep_id":"566","type":"conference","conference":{"location":"Sydney, Australia","end_date":"2013-12-08","start_date":"2013-12-01","name":"ICCV: International Conference on Computer Vision"},"ddc":["000"],"date_updated":"2021-01-12T06:56:28Z","file_date_updated":"2020-07-14T12:45:36Z","department":[{"_id":"VlKo"}],"quality_controlled":"1","publisher":"IEEE","oa":1,"day":"03","has_accepted_license":"1","year":"2014","date_published":"2014-03-03T00:00:00Z","doi":"10.1109/ICCV.2013.365","date_created":"2018-12-11T11:56:42Z","page":"2936 - 2943","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Olsson C, Ulen J, Boykov Y, Kolmogorov V. 2014. Partial enumeration and curvature regularization. ICCV: International Conference on Computer Vision, 2936–2943.","chicago":"Olsson, Carl, Johannes Ulen, Yuri Boykov, and Vladimir Kolmogorov. “Partial Enumeration and Curvature Regularization,” 2936–43. IEEE, 2014. https://doi.org/10.1109/ICCV.2013.365.","ama":"Olsson C, Ulen J, Boykov Y, Kolmogorov V. Partial enumeration and curvature regularization. In: IEEE; 2014:2936-2943. doi:10.1109/ICCV.2013.365","apa":"Olsson, C., Ulen, J., Boykov, Y., & Kolmogorov, V. (2014). Partial enumeration and curvature regularization (pp. 2936–2943). Presented at the ICCV: International Conference on Computer Vision, Sydney, Australia: IEEE. https://doi.org/10.1109/ICCV.2013.365","short":"C. Olsson, J. Ulen, Y. Boykov, V. Kolmogorov, in:, IEEE, 2014, pp. 2936–2943.","ieee":"C. Olsson, J. Ulen, Y. Boykov, and V. Kolmogorov, “Partial enumeration and curvature regularization,” presented at the ICCV: International Conference on Computer Vision, Sydney, Australia, 2014, pp. 2936–2943.","mla":"Olsson, Carl, et al. Partial Enumeration and Curvature Regularization. IEEE, 2014, pp. 2936–43, doi:10.1109/ICCV.2013.365."},"title":"Partial enumeration and curvature regularization","publist_id":"4669","author":[{"first_name":"Carl","full_name":"Olsson, Carl","last_name":"Olsson"},{"first_name":"Johannes","last_name":"Ulen","full_name":"Ulen, Johannes"},{"last_name":"Boykov","full_name":"Boykov, Yuri","first_name":"Yuri"},{"full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov","first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"}]},{"language":[{"iso":"eng"}],"day":"30","file":[{"checksum":"2b94e5e1f4c3fe8ab89b12806276fb09","file_id":"7039","content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2019-11-18T15:57:51Z","file_name":"2014_Playful_Math_Huszar.pdf","date_updated":"2020-07-14T12:47:48Z","file_size":511233,"creator":"dernst"}],"year":"2014","publication_status":"draft","has_accepted_license":"1","date_created":"2019-11-18T15:57:05Z","date_published":"2014-06-30T00:00:00Z","page":"5","oa_version":"Published Version","month":"06","oa":1,"publisher":"IST Austria","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["510"],"date_updated":"2020-07-14T23:11:45Z","citation":{"chicago":"Huszár, Kristóf, and Michal Rolinek. Playful Math - An Introduction to Mathematical Games. IST Austria, n.d.","ista":"Huszár K, Rolinek M. Playful Math - An introduction to mathematical games, IST Austria, 5p.","mla":"Huszár, Kristóf, and Michal Rolinek. Playful Math - An Introduction to Mathematical Games. IST Austria.","ieee":"K. Huszár and M. Rolinek, Playful Math - An introduction to mathematical games. IST Austria.","short":"K. Huszár, M. Rolinek, Playful Math - An Introduction to Mathematical Games, IST Austria, n.d.","ama":"Huszár K, Rolinek M. Playful Math - An Introduction to Mathematical Games. IST Austria","apa":"Huszár, K., & Rolinek, M. (n.d.). Playful Math - An introduction to mathematical games. IST Austria."},"title":"Playful Math - An introduction to mathematical games","file_date_updated":"2020-07-14T12:47:48Z","department":[{"_id":"VlKo"},{"_id":"UlWa"}],"article_processing_charge":"No","author":[{"first_name":"Kristóf","id":"33C26278-F248-11E8-B48F-1D18A9856A87","last_name":"Huszár","full_name":"Huszár, Kristóf","orcid":"0000-0002-5445-5057"},{"first_name":"Michal","id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87","last_name":"Rolinek","full_name":"Rolinek, Michal"}],"_id":"7038","status":"public","type":"working_paper"},{"citation":{"apa":"Bachrach, Y., Kohli, P., Kolmogorov, V., & Zadimoghaddam, M. (2013). Optimal Coalition Structures in Cooperative Graph Games (pp. 81–87). Presented at the AAAI: Conference on Artificial Intelligence, Bellevue, WA, United States: AAAI Press.","ama":"Bachrach Y, Kohli P, Kolmogorov V, Zadimoghaddam M. Optimal Coalition Structures in Cooperative Graph Games. In: AAAI Press; 2013:81-87.","short":"Y. Bachrach, P. Kohli, V. Kolmogorov, M. Zadimoghaddam, in:, AAAI Press, 2013, pp. 81–87.","ieee":"Y. Bachrach, P. Kohli, V. Kolmogorov, and M. Zadimoghaddam, “Optimal Coalition Structures in Cooperative Graph Games,” presented at the AAAI: Conference on Artificial Intelligence, Bellevue, WA, United States, 2013, pp. 81–87.","mla":"Bachrach, Yoram, et al. Optimal Coalition Structures in Cooperative Graph Games. AAAI Press, 2013, pp. 81–87.","ista":"Bachrach Y, Kohli P, Kolmogorov V, Zadimoghaddam M. 2013. Optimal Coalition Structures in Cooperative Graph Games. AAAI: Conference on Artificial Intelligence, 81–87.","chicago":"Bachrach, Yoram, Pushmeet Kohli, Vladimir Kolmogorov, and Morteza Zadimoghaddam. “Optimal Coalition Structures in Cooperative Graph Games,” 81–87. AAAI Press, 2013."},"date_updated":"2021-01-12T06:56:25Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["1108.5248"]},"publist_id":"4674","author":[{"full_name":"Bachrach, Yoram","last_name":"Bachrach","first_name":"Yoram"},{"first_name":"Pushmeet","last_name":"Kohli","full_name":"Kohli, Pushmeet"},{"first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","last_name":"Kolmogorov","full_name":"Kolmogorov, Vladimir"},{"last_name":"Zadimoghaddam","full_name":"Zadimoghaddam, Morteza","first_name":"Morteza"}],"title":"Optimal Coalition Structures in Cooperative Graph Games","department":[{"_id":"VlKo"}],"_id":"2270","conference":{"name":"AAAI: Conference on Artificial Intelligence","start_date":"2013-07-14","location":"Bellevue, WA, United States","end_date":"2013-07-18"},"type":"conference","status":"public","year":"2013","publication_status":"published","language":[{"iso":"eng"}],"day":"31","page":"81-87","date_created":"2018-12-11T11:56:41Z","date_published":"2013-12-31T00:00:00Z","abstract":[{"lang":"eng","text":"Representation languages for coalitional games are a key research area in algorithmic game theory. There is an inher-\r\nent tradeoff between how general a language is, allowing it to capture more elaborate games, and how hard it is computationally to optimize and solve such games. One prominent such language is the simple yet expressive\r\nWeighted Graph Games (WGGs) representation (Deng and Papadimitriou 1994), which maintains knowledge about synergies between agents in the form of an edge weighted graph. We consider the problem of finding the optimal coalition structure in WGGs. The agents in such games are vertices in a graph, and the value of a coalition is the sum of the weights of the edges present between coalition members. The optimal coalition structure is a partition of the agents to coalitions, that maximizes the sum of utilities obtained by the coalitions. We show that finding the optimal coalition structure is not only hard for general graphs, but is also intractable for restricted families such as planar graphs which are amenable for many other combinatorial problems. We then provide algorithms with constant factor approximations for planar, minorfree and bounded degree graphs."}],"oa_version":"None","oa":1,"main_file_link":[{"url":"http://arxiv.org/abs/1108.5248","open_access":"1"}],"publisher":"AAAI Press","quality_controlled":"1","month":"12"},{"month":"09","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1309.5655"}],"oa":1,"publisher":"IST Austria","quality_controlled":0,"abstract":[{"lang":"eng","text":"We propose a new family of message passing techniques for MAP estimation in graphical models which we call Sequential Reweighted Message Passing (SRMP). Special cases include well-known techniques such as Min-Sum Diusion (MSD) and a faster Sequential Tree-Reweighted Message Passing (TRW-S). Importantly, our derivation is simpler than the original derivation of TRW-S, and does not involve a decomposition into trees. This allows easy generalizations. We present such a generalization for the case of higher-order graphical models, and test it on several real-world problems with promising results."}],"date_created":"2018-12-11T11:56:42Z","date_published":"2013-09-22T00:00:00Z","day":"22","publication_status":"published","year":"2013","status":"public","type":"report","_id":"2273","title":"Reweighted message passing revisited","department":[{"_id":"VlKo"}],"author":[{"first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","last_name":"Kolmogorov","full_name":"Vladimir Kolmogorov"}],"publist_id":"4671","extern":0,"citation":{"mla":"Kolmogorov, Vladimir. Reweighted Message Passing Revisited. IST Austria, 2013.","short":"V. Kolmogorov, Reweighted Message Passing Revisited, IST Austria, 2013.","ieee":"V. Kolmogorov, Reweighted message passing revisited. IST Austria, 2013.","ama":"Kolmogorov V. Reweighted Message Passing Revisited. IST Austria; 2013.","apa":"Kolmogorov, V. (2013). Reweighted message passing revisited. IST Austria.","chicago":"Kolmogorov, Vladimir. Reweighted Message Passing Revisited. IST Austria, 2013.","ista":"Kolmogorov V. 2013. Reweighted message passing revisited, IST Austria,p."},"date_updated":"2019-01-24T13:07:32Z"},{"_id":"2276","status":"public","type":"conference","conference":{"start_date":"2013-12-01","location":"Sydney, Australia","end_date":"2013-12-08","name":"ICCV: International Conference on Computer Vision"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Gridchyn I, Kolmogorov V. 2013. Potts model, parametric maxflow and k-submodular functions. ICCV: International Conference on Computer Vision, 2320–2327.","chicago":"Gridchyn, Igor, and Vladimir Kolmogorov. “Potts Model, Parametric Maxflow and k-Submodular Functions,” 2320–27. IEEE, 2013. https://doi.org/10.1109/ICCV.2013.288.","short":"I. Gridchyn, V. Kolmogorov, in:, IEEE, 2013, pp. 2320–2327.","ieee":"I. Gridchyn and V. Kolmogorov, “Potts model, parametric maxflow and k-submodular functions,” presented at the ICCV: International Conference on Computer Vision, Sydney, Australia, 2013, pp. 2320–2327.","ama":"Gridchyn I, Kolmogorov V. Potts model, parametric maxflow and k-submodular functions. In: IEEE; 2013:2320-2327. doi:10.1109/ICCV.2013.288","apa":"Gridchyn, I., & Kolmogorov, V. (2013). Potts model, parametric maxflow and k-submodular functions (pp. 2320–2327). Presented at the ICCV: International Conference on Computer Vision, Sydney, Australia: IEEE. https://doi.org/10.1109/ICCV.2013.288","mla":"Gridchyn, Igor, and Vladimir Kolmogorov. Potts Model, Parametric Maxflow and k-Submodular Functions. IEEE, 2013, pp. 2320–27, doi:10.1109/ICCV.2013.288."},"date_updated":"2021-01-12T06:56:28Z","department":[{"_id":"JoCs"},{"_id":"VlKo"}],"title":"Potts model, parametric maxflow and k-submodular functions","publist_id":"4668","author":[{"full_name":"Gridchyn, Igor","last_name":"Gridchyn","id":"4B60654C-F248-11E8-B48F-1D18A9856A87","first_name":"Igor"},{"last_name":"Kolmogorov","full_name":"Kolmogorov, Vladimir","first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"arxiv":["1310.1771"]},"oa_version":"Preprint","abstract":[{"lang":"eng","text":"The problem of minimizing the Potts energy function frequently occurs in computer vision applications. One way to tackle this NP-hard problem was proposed by Kovtun [19, 20]. It identifies a part of an optimal solution by running k maxflow computations, where k is the number of labels. The number of “labeled” pixels can be significant in some applications, e.g. 50-93% in our tests for stereo. We show how to reduce the runtime to O (log k) maxflow computations (or one parametric maxflow computation). Furthermore, the output of our algorithm allows to speed-up the subsequent alpha expansion for the unlabeled part, or can be used as it is for time-critical applications. To derive our technique, we generalize the algorithm of Felzenszwalb et al. [7] for Tree Metrics . We also show a connection to k-submodular functions from combinatorial optimization, and discuss k-submodular relaxations for general energy functions."}],"month":"12","publisher":"IEEE","quality_controlled":"1","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1310.1771"}],"oa":1,"day":"01","language":[{"iso":"eng"}],"publication_status":"published","year":"2013","date_published":"2013-12-01T00:00:00Z","doi":"10.1109/ICCV.2013.288","date_created":"2018-12-11T11:56:43Z","page":"2320 - 2327"},{"author":[{"last_name":"Kolmogorov","full_name":"Kolmogorov, Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","first_name":"Vladimir"}],"publist_id":"4383","external_id":{"arxiv":["1207.7213"]},"title":"The power of linear programming for finite-valued CSPs: A constructive characterization","citation":{"ama":"Kolmogorov V. The power of linear programming for finite-valued CSPs: A constructive characterization. In: Vol 7965. Springer; 2013:625-636. doi:10.1007/978-3-642-39206-1_53","apa":"Kolmogorov, V. (2013). The power of linear programming for finite-valued CSPs: A constructive characterization (Vol. 7965, pp. 625–636). Presented at the ICALP: Automata, Languages and Programming, Riga, Latvia: Springer. https://doi.org/10.1007/978-3-642-39206-1_53","ieee":"V. Kolmogorov, “The power of linear programming for finite-valued CSPs: A constructive characterization,” presented at the ICALP: Automata, Languages and Programming, Riga, Latvia, 2013, vol. 7965, no. 1, pp. 625–636.","short":"V. Kolmogorov, in:, Springer, 2013, pp. 625–636.","mla":"Kolmogorov, Vladimir. The Power of Linear Programming for Finite-Valued CSPs: A Constructive Characterization. Vol. 7965, no. 1, Springer, 2013, pp. 625–36, doi:10.1007/978-3-642-39206-1_53.","ista":"Kolmogorov V. 2013. The power of linear programming for finite-valued CSPs: A constructive characterization. ICALP: Automata, Languages and Programming, LNCS, vol. 7965, 625–636.","chicago":"Kolmogorov, Vladimir. “The Power of Linear Programming for Finite-Valued CSPs: A Constructive Characterization,” 7965:625–36. Springer, 2013. https://doi.org/10.1007/978-3-642-39206-1_53."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publisher":"Springer","quality_controlled":"1","oa":1,"page":"625 - 636","doi":"10.1007/978-3-642-39206-1_53","date_published":"2013-07-01T00:00:00Z","date_created":"2018-12-11T11:58:08Z","year":"2013","day":"01","type":"conference","conference":{"location":"Riga, Latvia","end_date":"2013-07-12","start_date":"2013-07-08","name":"ICALP: Automata, Languages and Programming"},"status":"public","_id":"2518","department":[{"_id":"VlKo"}],"date_updated":"2023-02-23T10:35:42Z","alternative_title":["LNCS"],"scopus_import":1,"main_file_link":[{"url":"http://arxiv.org/abs/1207.7213","open_access":"1"}],"month":"07","intvolume":" 7965","abstract":[{"text":"A class of valued constraint satisfaction problems (VCSPs) is characterised by a valued constraint language, a fixed set of cost functions on a finite domain. An instance of the problem is specified by a sum of cost functions from the language with the goal to minimise the sum. We study which classes of finite-valued languages can be solved exactly by the basic linear programming relaxation (BLP). Thapper and Živný showed [20] that if BLP solves the language then the language admits a binary commutative fractional polymorphism. We prove that the converse is also true. This leads to a necessary and a sufficient condition which can be checked in polynomial time for a given language. In contrast, the previous necessary and sufficient condition due to [20] involved infinitely many inequalities. More recently, Thapper and Živný [21] showed (using, in particular, a technique introduced in this paper) that core languages that do not satisfy our condition are NP-hard. Taken together, these results imply that a finite-valued language can either be solved using Linear Programming or is NP-hard.","lang":"eng"}],"oa_version":"Preprint","related_material":{"record":[{"relation":"later_version","id":"2271","status":"public"}]},"volume":7965,"issue":"1","publication_status":"published","language":[{"iso":"eng"}]},{"oa":1,"publisher":"ACM","quality_controlled":"1","year":"2013","publication":"Journal of the ACM","day":"02","date_created":"2018-12-11T11:59:48Z","doi":"10.1145/2450142.2450146","date_published":"2013-04-02T00:00:00Z","article_number":"10","citation":{"mla":"Kolmogorov, Vladimir, and Stanislav Živný. “The Complexity of Conservative Valued CSPs.” Journal of the ACM, vol. 60, no. 2, 10, ACM, 2013, doi:10.1145/2450142.2450146.","ieee":"V. Kolmogorov and S. Živný, “The complexity of conservative valued CSPs,” Journal of the ACM, vol. 60, no. 2. ACM, 2013.","short":"V. Kolmogorov, S. Živný, Journal of the ACM 60 (2013).","apa":"Kolmogorov, V., & Živný, S. (2013). The complexity of conservative valued CSPs. Journal of the ACM. ACM. https://doi.org/10.1145/2450142.2450146","ama":"Kolmogorov V, Živný S. The complexity of conservative valued CSPs. Journal of the ACM. 2013;60(2). doi:10.1145/2450142.2450146","chicago":"Kolmogorov, Vladimir, and Stanislav Živný. “The Complexity of Conservative Valued CSPs.” Journal of the ACM. ACM, 2013. https://doi.org/10.1145/2450142.2450146.","ista":"Kolmogorov V, Živný S. 2013. The complexity of conservative valued CSPs. Journal of the ACM. 60(2), 10."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["1110.2809"]},"publist_id":"3971","author":[{"id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","first_name":"Vladimir","full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov"},{"first_name":"Stanislav","full_name":"Živný, Stanislav","last_name":"Živný"}],"title":"The complexity of conservative valued CSPs","abstract":[{"text":"We study the complexity of valued constraint satisfaction problems (VCSPs) parametrized by a constraint language, a fixed set of cost functions over a finite domain. An instance of the problem is specified by a sum of cost functions from the language and the goal is to minimize the sum. Under the unique games conjecture, the approximability of finite-valued VCSPs is well understood, see Raghavendra [2008]. However, there is no characterization of finite-valued VCSPs, let alone general-valued VCSPs, that can be solved exactly in polynomial time, thus giving insights from a combinatorial optimization perspective. We consider the case of languages containing all possible unary cost functions. In the case of languages consisting of only {0, ∞}-valued cost functions (i.e., relations), such languages have been called conservative and studied by Bulatov [2003, 2011] and recently by Barto [2011]. Since we study valued languages, we call a language conservative if it contains all finite-valued unary cost functions. The computational complexity of conservative valued languages has been studied by Cohen et al. [2006] for languages over Boolean domains, by Deineko et al. [2008] for {0, 1}-valued languages (a.k.a Max-CSP), and by Takhanov [2010a] for {0, ∞}-valued languages containing all finite-valued unary cost functions (a.k.a. Min-Cost-Hom). We prove a Schaefer-like dichotomy theorem for conservative valued languages: if all cost functions in the language satisfy a certain condition (specified by a complementary combination of STP and MJN multimor-phisms), then any instance can be solved in polynomial time (via a new algorithm developed in this article), otherwise the language is NP-hard. This is the first complete complexity classification of general-valued constraint languages over non-Boolean domains. It is a common phenomenon that complexity classifications of problems over non-Boolean domains are significantly harder than the Boolean cases. The polynomial-time algorithm we present for the tractable cases is a generalization of the submodular minimization problem and a result of Cohen et al. [2008]. Our results generalize previous results by Takhanov [2010a] and (a subset of results) by Cohen et al. [2006] and Deineko et al. [2008]. Moreover, our results do not rely on any computer-assisted search as in Deineko et al. [2008], and provide a powerful tool for proving hardness of finite-valued and general-valued languages.","lang":"eng"}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1110.2809"}],"scopus_import":1,"intvolume":" 60","month":"04","publication_status":"published","language":[{"iso":"eng"}],"volume":60,"issue":"2","_id":"2828","type":"journal_article","status":"public","date_updated":"2021-01-12T07:00:00Z","department":[{"_id":"VlKo"}]}]