[{"title":"The complexity of general-valued CSPs","author":[{"full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov","first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Krokhin","full_name":"Krokhin, Andrei","first_name":"Andrei"},{"last_name":"Rolinek","full_name":"Rolinek, Michal","first_name":"Michal","id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"7138","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Kolmogorov V, Krokhin A, Rolinek M. 2017. The complexity of general-valued CSPs. SIAM Journal on Computing. 46(3), 1087–1110.","chicago":"Kolmogorov, Vladimir, Andrei Krokhin, and Michal Rolinek. “The Complexity of General-Valued CSPs.” SIAM Journal on Computing. SIAM, 2017. https://doi.org/10.1137/16M1091836.","ama":"Kolmogorov V, Krokhin A, Rolinek M. The complexity of general-valued CSPs. SIAM Journal on Computing. 2017;46(3):1087-1110. doi:10.1137/16M1091836","apa":"Kolmogorov, V., Krokhin, A., & Rolinek, M. (2017). The complexity of general-valued CSPs. SIAM Journal on Computing. SIAM. https://doi.org/10.1137/16M1091836","short":"V. Kolmogorov, A. Krokhin, M. Rolinek, SIAM Journal on Computing 46 (2017) 1087–1110.","ieee":"V. Kolmogorov, A. Krokhin, and M. Rolinek, “The complexity of general-valued CSPs,” SIAM Journal on Computing, vol. 46, no. 3. SIAM, pp. 1087–1110, 2017.","mla":"Kolmogorov, Vladimir, et al. “The Complexity of General-Valued CSPs.” SIAM Journal on Computing, vol. 46, no. 3, SIAM, 2017, pp. 1087–110, doi:10.1137/16M1091836."},"project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160","_id":"25FBA906-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"date_created":"2018-12-11T11:47:40Z","doi":"10.1137/16M1091836","date_published":"2017-06-29T00:00:00Z","page":"1087 - 1110","publication":"SIAM Journal on Computing","day":"29","year":"2017","oa":1,"publisher":"SIAM","quality_controlled":"1","department":[{"_id":"VlKo"}],"date_updated":"2023-02-23T10:07:49Z","status":"public","type":"journal_article","_id":"644","ec_funded":1,"related_material":{"record":[{"relation":"other","id":"1637","status":"public"}]},"volume":46,"issue":"3","language":[{"iso":"eng"}],"publication_status":"published","intvolume":" 46","month":"06","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1502.07327"}],"scopus_import":1,"oa_version":"Preprint","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 6= 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 f0;1g 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 they are NP-hard. The case when all allowed functions take only finite values corresponds to a finitevalued 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 Živný. 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."}]},{"publication_identifier":{"isbn":["978-331958770-7"]},"publication_status":"published","language":[{"iso":"eng"}],"volume":10302,"ec_funded":1,"abstract":[{"text":"We present a novel convex relaxation and a corresponding inference algorithm for the non-binary discrete tomography problem, that is, reconstructing discrete-valued images from few linear measurements. In contrast to state of the art approaches that split the problem into a continuous reconstruction problem for the linear measurement constraints and a discrete labeling problem to enforce discrete-valued reconstructions, we propose a joint formulation that addresses both problems simultaneously, resulting in a tighter convex relaxation. For this purpose a constrained graphical model is set up and evaluated using a novel relaxation optimized by dual decomposition. We evaluate our approach experimentally and show superior solutions both mathematically (tighter relaxation) and experimentally in comparison to previously proposed relaxations.","lang":"eng"}],"oa_version":"Submitted Version","scopus_import":1,"alternative_title":["LNCS"],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1703.03769"}],"month":"06","intvolume":" 10302","date_updated":"2021-01-12T08:07:34Z","department":[{"_id":"VlKo"}],"_id":"646","type":"conference","conference":{"name":"SSVM: Scale Space and Variational Methods in Computer Vision","location":"Kolding, Denmark","end_date":"2017-06-08","start_date":"2017-06-04"},"status":"public","year":"2017","day":"01","page":"235 - 246","doi":"10.1007/978-3-319-58771-4_19","date_published":"2017-06-01T00:00:00Z","date_created":"2018-12-11T11:47:41Z","quality_controlled":"1","publisher":"Springer","oa":1,"citation":{"mla":"Kuske, Jan, et al. A Novel Convex Relaxation for Non Binary Discrete Tomography. Edited by François Lauze et al., vol. 10302, Springer, 2017, pp. 235–46, doi:10.1007/978-3-319-58771-4_19.","ieee":"J. Kuske, P. Swoboda, and S. Petra, “A novel convex relaxation for non binary discrete tomography,” presented at the SSVM: Scale Space and Variational Methods in Computer Vision, Kolding, Denmark, 2017, vol. 10302, pp. 235–246.","short":"J. Kuske, P. Swoboda, S. Petra, in:, F. Lauze, Y. Dong, A. Bjorholm Dahl (Eds.), Springer, 2017, pp. 235–246.","apa":"Kuske, J., Swoboda, P., & Petra, S. (2017). A novel convex relaxation for non binary discrete tomography. In F. Lauze, Y. Dong, & A. Bjorholm Dahl (Eds.) (Vol. 10302, pp. 235–246). Presented at the SSVM: Scale Space and Variational Methods in Computer Vision, Kolding, Denmark: Springer. https://doi.org/10.1007/978-3-319-58771-4_19","ama":"Kuske J, Swoboda P, Petra S. A novel convex relaxation for non binary discrete tomography. In: Lauze F, Dong Y, Bjorholm Dahl A, eds. Vol 10302. Springer; 2017:235-246. doi:10.1007/978-3-319-58771-4_19","chicago":"Kuske, Jan, Paul Swoboda, and Stefanie Petra. “A Novel Convex Relaxation for Non Binary Discrete Tomography.” edited by François Lauze, Yiqiu Dong, and Anders Bjorholm Dahl, 10302:235–46. Springer, 2017. https://doi.org/10.1007/978-3-319-58771-4_19.","ista":"Kuske J, Swoboda P, Petra S. 2017. A novel convex relaxation for non binary discrete tomography. SSVM: Scale Space and Variational Methods in Computer Vision, LNCS, vol. 10302, 235–246."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Kuske","full_name":"Kuske, Jan","first_name":"Jan"},{"full_name":"Swoboda, Paul","last_name":"Swoboda","first_name":"Paul","id":"446560C6-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Stefanie","full_name":"Petra, Stefanie","last_name":"Petra"}],"publist_id":"7132","title":"A novel convex relaxation for non binary discrete tomography","editor":[{"first_name":"François","full_name":"Lauze, François","last_name":"Lauze"},{"first_name":"Yiqiu","full_name":"Dong, Yiqiu","last_name":"Dong"},{"full_name":"Bjorholm Dahl, Anders","last_name":"Bjorholm Dahl","first_name":"Anders"}],"project":[{"call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425","name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160"}]},{"_id":"992","type":"dissertation","status":"public","pubrep_id":"815","supervisor":[{"full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov","first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2023-09-07T12:05:41Z","ddc":["004"],"department":[{"_id":"VlKo"}],"file_date_updated":"2020-07-14T12:48:18Z","abstract":[{"text":"An instance of the Constraint Satisfaction Problem (CSP) is given by a finite set of\r\nvariables, a finite domain of labels, and a set of constraints, each constraint acting on\r\na subset of the variables. The goal is to find an assignment of labels to its variables\r\nthat satisfies all constraints (or decide whether one exists). If we allow more general\r\n“soft” constraints, which come with (possibly infinite) costs of particular assignments,\r\nwe obtain instances from a richer class called Valued Constraint Satisfaction Problem\r\n(VCSP). There the goal is to find an assignment with minimum total cost.\r\nIn this thesis, we focus (assuming that P\r\n6\r\n=\r\nNP) on classifying computational com-\r\nplexity of CSPs and VCSPs under certain restricting conditions. Two results are the core\r\ncontent of the work. In one of them, we consider VCSPs parametrized by a constraint\r\nlanguage, that is the set of “soft” constraints allowed to form the instances, and finish\r\nthe complexity classification modulo (missing pieces of) complexity classification for\r\nanalogously parametrized CSP. The other result is a generalization of Edmonds’ perfect\r\nmatching algorithm. This generalization contributes to complexity classfications in two\r\nways. First, it gives a new (largest known) polynomial-time solvable class of Boolean\r\nCSPs in which every variable may appear in at most two constraints and second, it\r\nsettles full classification of Boolean CSPs with planar drawing (again parametrized by a\r\nconstraint language).","lang":"eng"}],"oa_version":"Published Version","alternative_title":["ISTA Thesis"],"month":"05","publication_identifier":{"issn":["2663-337X"]},"degree_awarded":"PhD","publication_status":"published","file":[{"file_size":786145,"date_updated":"2020-07-14T12:48:18Z","creator":"system","file_name":"IST-2017-815-v1+3_final_blank_signature_maybe_pdfa.pdf","date_created":"2018-12-12T10:07:55Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_id":"4654","checksum":"81761fb939acb7585c36629f765b4373"},{"creator":"dernst","file_size":5936337,"date_updated":"2020-07-14T12:48:18Z","file_name":"2017_Thesis_Rolinek_source.zip","date_created":"2019-04-05T08:43:24Z","relation":"source_file","access_level":"closed","content_type":"application/zip","checksum":"2b2d7e1d6c1c79a9795a7aa0f860baf3","file_id":"6208"}],"language":[{"iso":"eng"}],"ec_funded":1,"project":[{"grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice","call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425"}],"citation":{"short":"M. Rolinek, Complexity of Constraint Satisfaction, Institute of Science and Technology Austria, 2017.","ieee":"M. Rolinek, “Complexity of constraint satisfaction,” Institute of Science and Technology Austria, 2017.","ama":"Rolinek M. Complexity of constraint satisfaction. 2017. doi:10.15479/AT:ISTA:th_815","apa":"Rolinek, M. (2017). Complexity of constraint satisfaction. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th_815","mla":"Rolinek, Michal. Complexity of Constraint Satisfaction. Institute of Science and Technology Austria, 2017, doi:10.15479/AT:ISTA:th_815.","ista":"Rolinek M. 2017. Complexity of constraint satisfaction. Institute of Science and Technology Austria.","chicago":"Rolinek, Michal. “Complexity of Constraint Satisfaction.” Institute of Science and Technology Austria, 2017. https://doi.org/10.15479/AT:ISTA:th_815."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publist_id":"6407","author":[{"last_name":"Rolinek","full_name":"Rolinek, Michal","first_name":"Michal","id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","title":"Complexity of constraint satisfaction","acknowledgement":"FP7/2007-2013/ERC grant agreement no 616160","publisher":"Institute of Science and Technology Austria","oa":1,"has_accepted_license":"1","year":"2017","day":"01","page":"97","doi":"10.15479/AT:ISTA:th_815","date_published":"2017-05-01T00:00:00Z","date_created":"2018-12-11T11:49:35Z"},{"language":[{"iso":"eng"}],"publication_identifier":{"isbn":["978-161197478-2"]},"publication_status":"published","related_material":{"record":[{"status":"public","id":"6032","relation":"later_version"}]},"ec_funded":1,"oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"The main result of this paper is a generalization of the classical blossom algorithm for finding perfect matchings. Our algorithm can efficiently solve Boolean CSPs where each variable appears in exactly two constraints (we call it edge CSP) and all constraints are even Δ-matroid relations (represented by lists of tuples). As a consequence of this, we settle the complexity classification of planar Boolean CSPs started by Dvorak and Kupec. Knowing that edge CSP is tractable for even Δ-matroid constraints allows us to extend the tractability result to a larger class of Δ-matroids that includes many classes that were known to be tractable before, namely co-independent, compact, local and binary."}],"month":"01","main_file_link":[{"url":"https://arxiv.org/abs/1602.03124","open_access":"1"}],"date_updated":"2023-09-20T11:20:26Z","department":[{"_id":"VlKo"}],"_id":"1192","status":"public","type":"conference","conference":{"start_date":"2017-01-16","end_date":"2017-01019","location":"Barcelona, Spain","name":"SODA: Symposium on Discrete Algorithms"},"day":"01","isi":1,"year":"2017","doi":"10.1137/1.9781611974782.20","date_published":"2017-01-01T00:00:00Z","date_created":"2018-12-11T11:50:38Z","page":"307 - 326","publisher":"SIAM","quality_controlled":"1","oa":1,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ista":"Kazda A, Kolmogorov V, Rolinek M. 2017. Even delta-matroids and the complexity of planar Boolean CSPs. SODA: Symposium on Discrete Algorithms, 307–326.","chicago":"Kazda, Alexandr, Vladimir Kolmogorov, and Michal Rolinek. “Even Delta-Matroids and the Complexity of Planar Boolean CSPs,” 307–26. SIAM, 2017. https://doi.org/10.1137/1.9781611974782.20.","ieee":"A. Kazda, V. Kolmogorov, and M. Rolinek, “Even delta-matroids and the complexity of planar Boolean CSPs,” presented at the SODA: Symposium on Discrete Algorithms, Barcelona, Spain, 2017, pp. 307–326.","short":"A. Kazda, V. Kolmogorov, M. Rolinek, in:, SIAM, 2017, pp. 307–326.","apa":"Kazda, A., Kolmogorov, V., & Rolinek, M. (2017). Even delta-matroids and the complexity of planar Boolean CSPs (pp. 307–326). Presented at the SODA: Symposium on Discrete Algorithms, Barcelona, Spain: SIAM. https://doi.org/10.1137/1.9781611974782.20","ama":"Kazda A, Kolmogorov V, Rolinek M. Even delta-matroids and the complexity of planar Boolean CSPs. In: SIAM; 2017:307-326. doi:10.1137/1.9781611974782.20","mla":"Kazda, Alexandr, et al. Even Delta-Matroids and the Complexity of Planar Boolean CSPs. SIAM, 2017, pp. 307–26, doi:10.1137/1.9781611974782.20."},"title":"Even delta-matroids and the complexity of planar Boolean CSPs","author":[{"first_name":"Alexandr","id":"3B32BAA8-F248-11E8-B48F-1D18A9856A87","full_name":"Kazda, Alexandr","last_name":"Kazda"},{"full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov","first_name":"Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Michal","id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87","last_name":"Rolinek","full_name":"Rolinek, Michal"}],"publist_id":"6159","external_id":{"isi":["000426965800020"]},"article_processing_charge":"No","project":[{"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":"2017-07-21","end_date":"2017-07-26","location":"Honolulu, HA, United States","name":"CVPR: Computer Vision and Pattern Recognition"},"type":"conference","_id":"916","department":[{"_id":"VlKo"}],"file_date_updated":"2020-07-14T12:48:15Z","ddc":["000"],"date_updated":"2023-09-26T15:41:40Z","intvolume":" 2017","month":"01","scopus_import":"1","oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"We study the quadratic assignment problem, in computer vision also known as graph matching. Two leading solvers for this problem optimize the Lagrange decomposition duals with sub-gradient and dual ascent (also known as message passing) updates. We explore this direction further and propose several additional Lagrangean relaxations of the graph matching problem along with corresponding algorithms, which are all based on a common dual ascent framework. Our extensive empirical evaluation gives several theoretical insights and suggests a new state-of-the-art anytime solver for the considered problem. Our improvement over state-of-the-art is particularly visible on a new dataset with large-scale sparse problem instances containing more than 500 graph nodes each."}],"ec_funded":1,"volume":2017,"language":[{"iso":"eng"}],"file":[{"creator":"dernst","file_size":944332,"date_updated":"2020-07-14T12:48:15Z","file_name":"2017_CVPR_Swoboda2.pdf","date_created":"2019-01-18T12:49:38Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","checksum":"e38a2740daad1ea178465843b5072906","file_id":"5848"}],"publication_status":"published","publication_identifier":{"isbn":["978-153860457-1"]},"project":[{"name":"Discrete Optimization in Computer Vision: Theory and Practice","grant_number":"616160","call_identifier":"FP7","_id":"25FBA906-B435-11E9-9278-68D0E5697425"}],"title":"A study of lagrangean decompositions and dual ascent solvers for graph matching","external_id":{"isi":["000418371407018"]},"article_processing_charge":"No","publist_id":"6525","author":[{"first_name":"Paul","id":"446560C6-F248-11E8-B48F-1D18A9856A87","last_name":"Swoboda","full_name":"Swoboda, Paul"},{"first_name":"Carsten","last_name":"Rother","full_name":"Rother, Carsten"},{"full_name":"Abu Alhaija, Carsten","last_name":"Abu Alhaija","first_name":"Carsten"},{"full_name":"Kainmueller, Dagmar","last_name":"Kainmueller","first_name":"Dagmar"},{"first_name":"Bogdan","last_name":"Savchynskyy","full_name":"Savchynskyy, Bogdan"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Swoboda, Paul, et al. A Study of Lagrangean Decompositions and Dual Ascent Solvers for Graph Matching. Vol. 2017, IEEE, 2017, pp. 7062–71, doi:10.1109/CVPR.2017.747.","ieee":"P. Swoboda, C. Rother, C. Abu Alhaija, D. Kainmueller, and B. Savchynskyy, “A study of lagrangean decompositions and dual ascent solvers for graph matching,” presented at the CVPR: Computer Vision and Pattern Recognition, Honolulu, HA, United States, 2017, vol. 2017, pp. 7062–7071.","short":"P. Swoboda, C. Rother, C. Abu Alhaija, D. Kainmueller, B. Savchynskyy, in:, IEEE, 2017, pp. 7062–7071.","apa":"Swoboda, P., Rother, C., Abu Alhaija, C., Kainmueller, D., & Savchynskyy, B. (2017). A study of lagrangean decompositions and dual ascent solvers for graph matching (Vol. 2017, pp. 7062–7071). Presented at the CVPR: Computer Vision and Pattern Recognition, Honolulu, HA, United States: IEEE. https://doi.org/10.1109/CVPR.2017.747","ama":"Swoboda P, Rother C, Abu Alhaija C, Kainmueller D, Savchynskyy B. A study of lagrangean decompositions and dual ascent solvers for graph matching. In: Vol 2017. IEEE; 2017:7062-7071. doi:10.1109/CVPR.2017.747","chicago":"Swoboda, Paul, Carsten Rother, Carsten Abu Alhaija, Dagmar Kainmueller, and Bogdan Savchynskyy. “A Study of Lagrangean Decompositions and Dual Ascent Solvers for Graph Matching,” 2017:7062–71. IEEE, 2017. https://doi.org/10.1109/CVPR.2017.747.","ista":"Swoboda P, Rother C, Abu Alhaija C, Kainmueller D, Savchynskyy B. 2017. A study of lagrangean decompositions and dual ascent solvers for graph matching. CVPR: Computer Vision and Pattern Recognition vol. 2017, 7062–7071."},"oa":1,"publisher":"IEEE","quality_controlled":"1","date_created":"2018-12-11T11:49:11Z","date_published":"2017-01-01T00:00:00Z","doi":"10.1109/CVPR.2017.747","page":"7062-7071","day":"01","year":"2017","has_accepted_license":"1","isi":1}]