@article{5975, abstract = {We consider the recent formulation of the algorithmic Lov ́asz Local Lemma [N. Har-vey and J. Vondr ́ak, inProceedings of FOCS, 2015, pp. 1327–1345; D. Achlioptas and F. Iliopoulos,inProceedings of SODA, 2016, pp. 2024–2038; D. Achlioptas, F. Iliopoulos, and V. Kolmogorov,ALocal Lemma for Focused Stochastic Algorithms, arXiv preprint, 2018] for finding objects that avoid“bad features,” or “flaws.” It extends the Moser–Tardos resampling algorithm [R. A. Moser andG. Tardos,J. ACM, 57 (2010), 11] to more general discrete spaces. At each step the method picks aflaw present in the current state and goes to a new state according to some prespecified probabilitydistribution (which depends on the current state and the selected flaw). However, the recent formu-lation is less flexible than the Moser–Tardos method since it requires a specific flaw selection rule,whereas the algorithm of Moser and Tardos allows an arbitrary rule (and thus can potentially beimplemented more efficiently). We formulate a new “commutativity” condition and prove that it issufficient for an arbitrary rule to work. It also enables an efficient parallelization under an additionalassumption. We then show that existing resampling oracles for perfect matchings and permutationsdo satisfy this condition.}, author = {Kolmogorov, Vladimir}, issn = {1095-7111}, journal = {SIAM Journal on Computing}, number = {6}, pages = {2029--2056}, publisher = {Society for Industrial & Applied Mathematics (SIAM)}, title = {{Commutativity in the algorithmic Lovász local lemma}}, doi = {10.1137/16m1093306}, volume = {47}, year = {2018}, } @inproceedings{5978, abstract = {We consider the MAP-inference problem for graphical models,which is a valued constraint satisfaction problem defined onreal numbers with a natural summation operation. We proposea family of relaxations (different from the famous Sherali-Adams hierarchy), which naturally define lower bounds for itsoptimum. This family always contains a tight relaxation andwe give an algorithm able to find it and therefore, solve theinitial non-relaxed NP-hard problem.The relaxations we consider decompose the original probleminto two non-overlapping parts: an easy LP-tight part and adifficult one. For the latter part a combinatorial solver must beused. As we show in our experiments, in a number of applica-tions the second, difficult part constitutes only a small fractionof the whole problem. This property allows to significantlyreduce the computational time of the combinatorial solver andtherefore solve problems which were out of reach before.}, author = {Haller, Stefan and Swoboda, Paul and Savchynskyy, Bogdan}, booktitle = {Proceedings of the 32st AAAI Conference on Artificial Intelligence}, location = {New Orleans, LU, United States}, pages = {6581--6588}, publisher = {AAAI Press}, title = {{Exact MAP-inference by confining combinatorial search with LP relaxation}}, year = {2018}, } @article{18, abstract = {An N-superconcentrator is a directed, acyclic graph with N input nodes and N output nodes such that every subset of the inputs and every subset of the outputs of same cardinality can be connected by node-disjoint paths. It is known that linear-size and bounded-degree superconcentrators exist. We prove the existence of such superconcentrators with asymptotic density 25.3 (where the density is the number of edges divided by N). The previously best known densities were 28 [12] and 27.4136 [17].}, author = {Kolmogorov, Vladimir and Rolinek, Michal}, issn = {0381-7032}, journal = {Ars Combinatoria}, number = {10}, pages = {269 -- 304}, publisher = {Charles Babbage Research Centre}, title = {{Superconcentrators of density 25.3}}, volume = {141}, year = {2018}, } @article{6032, abstract = {The main result of this article 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. Using a reduction to even Δ-matroids, we then extend the tractability result to larger classes of Δ-matroids that we call efficiently coverable. It properly includes classes that were known to be tractable before, namely, co-independent, compact, local, linear, and binary, with the following caveat:We represent Δ-matroids by lists of tuples, while the last two use a representation by matrices. Since an n ×n matrix can represent exponentially many tuples, our tractability result is not strictly stronger than the known algorithm for linear and binary Δ-matroids.}, author = {Kazda, Alexandr and Kolmogorov, Vladimir and Rolinek, Michal}, journal = {ACM Transactions on Algorithms}, number = {2}, publisher = {ACM}, title = {{Even delta-matroids and the complexity of planar boolean CSPs}}, doi = {10.1145/3230649}, volume = {15}, year = {2018}, } @misc{5573, abstract = {Graph matching problems for large displacement optical flow of RGB-D images.}, author = {Alhaija, Hassan and Sellent, Anita and Kondermann, Daniel and Rother, Carsten}, keywords = {graph matching, quadratic assignment problem<}, publisher = {Institute of Science and Technology Austria}, title = {{Graph matching problems for GraphFlow – 6D Large Displacement Scene Flow}}, doi = {10.15479/AT:ISTA:82}, year = {2018}, } @inproceedings{641, abstract = {We introduce two novel methods for learning parameters of graphical models for image labelling. The following two tasks underline both methods: (i) perturb model parameters based on given features and ground truth labelings, so as to exactly reproduce these labelings as optima of the local polytope relaxation of the labelling problem; (ii) train a predictor for the perturbed model parameters so that improved model parameters can be applied to the labelling of novel data. Our first method implements task (i) by inverse linear programming and task (ii) using a regressor e.g. a Gaussian process. Our second approach simultaneously solves tasks (i) and (ii) in a joint manner, while being restricted to linearly parameterised predictors. Experiments demonstrate the merits of both approaches.}, author = {Trajkovska, Vera and Swoboda, Paul and Åström, Freddie and Petra, Stefanie}, editor = {Lauze, François and Dong, Yiqiu and Bjorholm Dahl, Anders}, isbn = {978-331958770-7}, location = {Kolding, Denmark}, pages = {323 -- 334}, publisher = {Springer}, title = {{Graphical model parameter learning by inverse linear programming}}, doi = {10.1007/978-3-319-58771-4_26}, volume = {10302}, year = {2017}, } @article{644, abstract = {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.}, author = {Kolmogorov, Vladimir and Krokhin, Andrei and Rolinek, Michal}, journal = {SIAM Journal on Computing}, number = {3}, pages = {1087 -- 1110}, publisher = {SIAM}, title = {{The complexity of general-valued CSPs}}, doi = {10.1137/16M1091836}, volume = {46}, year = {2017}, } @inproceedings{646, abstract = {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.}, author = {Kuske, Jan and Swoboda, Paul and Petra, Stefanie}, editor = {Lauze, François and Dong, Yiqiu and Bjorholm Dahl, Anders}, isbn = {978-331958770-7}, location = {Kolding, Denmark}, pages = {235 -- 246}, publisher = {Springer}, title = {{A novel convex relaxation for non binary discrete tomography}}, doi = {10.1007/978-3-319-58771-4_19}, volume = {10302}, year = {2017}, } @phdthesis{992, abstract = {An instance of the Constraint Satisfaction Problem (CSP) is given by a finite set of variables, a finite domain of labels, and a set of constraints, each constraint acting on a subset of the variables. The goal is to find an assignment of labels to its variables that satisfies all constraints (or decide whether one exists). If we allow more general “soft” constraints, which come with (possibly infinite) costs of particular assignments, we obtain instances from a richer class called Valued Constraint Satisfaction Problem (VCSP). There the goal is to find an assignment with minimum total cost. In this thesis, we focus (assuming that P 6 = NP) on classifying computational com- plexity of CSPs and VCSPs under certain restricting conditions. Two results are the core content of the work. In one of them, we consider VCSPs parametrized by a constraint language, that is the set of “soft” constraints allowed to form the instances, and finish the complexity classification modulo (missing pieces of) complexity classification for analogously parametrized CSP. The other result is a generalization of Edmonds’ perfect matching algorithm. This generalization contributes to complexity classfications in two ways. First, it gives a new (largest known) polynomial-time solvable class of Boolean CSPs in which every variable may appear in at most two constraints and second, it settles full classification of Boolean CSPs with planar drawing (again parametrized by a constraint language).}, author = {Rolinek, Michal}, issn = {2663-337X}, pages = {97}, publisher = {Institute of Science and Technology Austria}, title = {{Complexity of constraint satisfaction}}, doi = {10.15479/AT:ISTA:th_815}, year = {2017}, } @inproceedings{1192, abstract = {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.}, author = {Kazda, Alexandr and Kolmogorov, Vladimir and Rolinek, Michal}, isbn = {978-161197478-2}, location = {Barcelona, Spain}, pages = {307 -- 326}, publisher = {SIAM}, title = {{Even delta-matroids and the complexity of planar Boolean CSPs}}, doi = {10.1137/1.9781611974782.20}, year = {2017}, } @inproceedings{916, abstract = {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.}, author = {Swoboda, Paul and Rother, Carsten and Abu Alhaija, Carsten and Kainmueller, Dagmar and Savchynskyy, Bogdan}, isbn = {978-153860457-1}, location = {Honolulu, HA, United States}, pages = {7062--7071}, publisher = {IEEE}, title = {{A study of lagrangean decompositions and dual ascent solvers for graph matching}}, doi = {10.1109/CVPR.2017.747}, volume = {2017}, year = {2017}, } @inproceedings{915, abstract = {We propose a dual decomposition and linear program relaxation of the NP-hard minimum cost multicut problem. Unlike other polyhedral relaxations of the multicut polytope, it is amenable to efficient optimization by message passing. Like other polyhedral relaxations, it can be tightened efficiently by cutting planes. We define an algorithm that alternates between message passing and efficient separation of cycle- and odd-wheel inequalities. This algorithm is more efficient than state-of-the-art algorithms based on linear programming, including algorithms written in the framework of leading commercial software, as we show in experiments with large instances of the problem from applications in computer vision, biomedical image analysis and data mining.}, author = {Swoboda, Paul and Andres, Bjoern}, isbn = {978-153860457-1}, location = {Honolulu, HA, United States}, pages = {4990--4999}, publisher = {IEEE}, title = {{A message passing algorithm for the minimum cost multicut problem}}, doi = {10.1109/CVPR.2017.530}, volume = {2017}, year = {2017}, } @inproceedings{917, abstract = {We propose a general dual ascent framework for Lagrangean decomposition of combinatorial problems. Although methods of this type have shown their efficiency for a number of problems, so far there was no general algorithm applicable to multiple problem types. In this work, we propose such a general algorithm. It depends on several parameters, which can be used to optimize its performance in each particular setting. We demonstrate efficacy of our method on graph matching and multicut problems, where it outperforms state-of-the-art solvers including those based on subgradient optimization and off-the-shelf linear programming solvers.}, author = {Swoboda, Paul and Kuske, Jan and Savchynskyy, Bogdan}, isbn = {978-153860457-1}, location = {Honolulu, HA, United States}, pages = {4950--4960}, publisher = {IEEE}, title = {{A dual ascent framework for Lagrangean decomposition of combinatorial problems}}, doi = {10.1109/CVPR.2017.526}, volume = {2017}, year = {2017}, } @inproceedings{274, abstract = {We consider the problem of estimating the partition function Z(β)=∑xexp(−β(H(x)) of a Gibbs distribution with a Hamilton H(⋅), or more precisely the logarithm of the ratio q=lnZ(0)/Z(β). It has been recently shown how to approximate q with high probability assuming the existence of an oracle that produces samples from the Gibbs distribution for a given parameter value in [0,β]. The current best known approach due to Huber [9] uses O(qlnn⋅[lnq+lnlnn+ε−2]) oracle calls on average where ε is the desired accuracy of approximation and H(⋅) is assumed to lie in {0}∪[1,n]. We improve the complexity to O(qlnn⋅ε−2) oracle calls. We also show that the same complexity can be achieved if exact oracles are replaced with approximate sampling oracles that are within O(ε2qlnn) variation distance from exact oracles. Finally, we prove a lower bound of Ω(q⋅ε−2) oracle calls under a natural model of computation.}, author = {Kolmogorov, Vladimir}, booktitle = {Proceedings of the 31st Conference On Learning Theory}, pages = {228--249}, publisher = {ML Research Press}, title = {{A faster approximation algorithm for the Gibbs partition function}}, volume = {75}, year = {2017}, } @misc{5561, abstract = {Graph matching problems as described in "Active Graph Matching for Automatic Joint Segmentation and Annotation of C. Elegans." by Kainmueller, Dagmar and Jug, Florian and Rother, Carsten and Myers, Gene, MICCAI 2014. Problems are in OpenGM2 hdf5 format (see http://hciweb2.iwr.uni-heidelberg.de/opengm/) and a custom text format used by the feature matching solver described in "Feature Correspondence via Graph Matching: Models and Global Optimization." by Lorenzo Torresani, Vladimir Kolmogorov and Carsten Rother, ECCV 2008, code at http://pub.ist.ac.at/~vnk/software/GraphMatching-v1.02.src.zip. }, author = {Kainmueller, Dagmar and Jug, Florian and Rother, Carsten and Meyers, Gene}, keywords = {graph matching, feature matching, QAP, MAP-inference}, publisher = {Institute of Science and Technology Austria}, title = {{Graph matching problems for annotating C. Elegans}}, doi = {10.15479/AT:ISTA:57}, year = {2017}, } @inproceedings{1231, abstract = {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).}, author = {Alwen, Joel F and Chen, Binyi and Kamath Hosdurg, Chethan and Kolmogorov, Vladimir and Pietrzak, Krzysztof Z and Tessaro, Stefano}, location = {Vienna, Austria}, pages = {358 -- 387}, publisher = {Springer}, title = {{On the complexity of scrypt and proofs of space in the parallel random oracle model}}, doi = {10.1007/978-3-662-49896-5_13}, volume = {9666}, year = {2016}, } @article{1353, abstract = {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.}, author = {Barto, Libor and Kazda, Alexandr}, journal = {International Journal of Algebra and Computation}, number = {5}, pages = {1033 -- 1060}, publisher = {World Scientific Publishing}, title = {{Deciding absorption}}, doi = {10.1142/S0218196716500430}, volume = {26}, year = {2016}, } @article{1377, abstract = {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.}, author = {Kolmogorov, Vladimir and Pock, Thomas and Rolinek, Michal}, journal = {SIAM Journal on Imaging Sciences}, number = {2}, pages = {605 -- 636}, publisher = {Society for Industrial and Applied Mathematics }, title = {{Total variation on a tree}}, doi = {10.1137/15M1010257}, volume = {9}, year = {2016}, } @article{1612, abstract = {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).}, author = {Kazda, Alexandr}, journal = {Algebra Universalis}, number = {1}, pages = {75 -- 84}, publisher = {Springer}, title = {{CSP for binary conservative relational structures}}, doi = {10.1007/s00012-015-0358-8}, volume = {75}, year = {2016}, } @inproceedings{1193, abstract = {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.}, author = {Kolmogorov, Vladimir}, booktitle = {Proceedings - Annual IEEE Symposium on Foundations of Computer Science}, location = {New Brunswick, NJ, USA }, publisher = {IEEE}, title = {{Commutativity in the algorithmic Lovasz local lemma}}, doi = {10.1109/FOCS.2016.88}, volume = {2016-December}, year = {2016}, }