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The Power of the Combined Basic LP and Affine Relaxation for Promise CSPs [article]

Joshua Brakensiek, Venkatesan Guruswami, Marcin Wrochna, Stanislav Živný
2020 arXiv   pre-print
In the field of constraint satisfaction problems (CSP), promise CSPs are an exciting new direction of study.  ...  This generalizes previous work of the first two authors [BG19]. We also extend this algorithm to a more general class of block-symmetric polymorphisms.  ...  A From Relaxations to Minion Homomorphisms In this appendix, we recall the definition of the minion Q conv and prove Lemma 7 from Section 5.  ... 
arXiv:1907.04383v3 fatcat:uw43kazqtrcnlnsobu5cg4gvty

The Combined Basic LP and Affine IP Relaxation for Promise VCSPs on Infinite Domains

Caterina Viola, Stanislav Živný, Daniel Kráľ, Javier Esparza
2020 International Symposium on Mathematical Foundations of Computer Science  
This extends a result of Brakensiek and Guruswami [SODA'20] for promise (non-valued) CSPs (on finite domains).  ...  relaxation for exact solvability of promise valued CSPs over infinite-domains.  ...  For finite-domain PCSPs, the condition of having a block-symmetric promise polymorphism of arity 2L + 1 is equivalent to the one of having a block-symmetric promise polymorphism of arity 2L + 1 with two  ... 
doi:10.4230/lipics.mfcs.2020.85 dblp:conf/mfcs/ViolaZ20 fatcat:xtzypvd7hbck3lyhyg6vgryntq

The combined basic LP and affine IP relaxation for promise VCSPs on infinite domains [article]

Caterina Viola, Stanislav Zivny
2021 arXiv   pre-print
This extends a result of Brakensiek and Guruswami [SODA'20] for promise (non-valued) CSPs (on finite domains).  ...  relaxation for exact solvability of promise valued CSPs over infinite-domains.  ...  Let ω be the (2L + 1)-ary block-symmetric promise fractional polymorphism of (∆, Γ) with symmetric blocks B 1 and B 2 of size L + 1 and L, respectively.  ... 
arXiv:2007.01779v2 fatcat:jiweubnh35clngysvhyi3azjhu

An Algorithmic Blend of LPs and Ring Equations for Promise CSPs [article]

Joshua Brakensiek, Venkatesan Guruswami
2018 arXiv   pre-print
Similar to CSPs, the tractability of promise CSPs can be tied to the structure of operations on the solution space called polymorphisms, though in the promise world these operations are much less constrained  ...  The rounding step is intimately tied to the family of polymorphisms and clarifies the connection between polymorphisms and algorithms in this context.  ...  The authors also thank Libor Barto, Andrei Krokhin and Jakub Opršal for a myriad of helpful comments on this paper at Dagstuhl Seminar 18231 on "The Constraint Satisfaction Problem: Complexity and Approximability  ... 
arXiv:1807.05194v1 fatcat:wptigingdref3kv6oasx5xtmce

The Constraint Satisfaction Problem: Complexity and Approximability (Dagstuhl Seminar 18231)

Martin Grohe, Venkatesan Guruswami, Stanislav Zivny, Michael Wagner
2018 Dagstuhl Reports  
CSPs constitute a very rich and yet sufficiently manageable class of problems to give a good perspective on general computational phenomena.  ...  Constraint satisfaction has always played a central role in computational complexity theory; appropriate versions of CSPs are classical complete problems for most standard complexity classes.  ...  -The Constraint Satisfaction Problem: Complexity and Approximability From Weak to Strong LP Gaps for all CSPs We study the approximability of constraint satisfaction problems (CSPs) by linear programming  ... 
doi:10.4230/dagrep.8.6.1 dblp:journals/dagstuhl-reports/GroheGZ18 fatcat:3bqo62ly3rgzlnh3bmkvwbuwea

The Power of the Combined Basic Linear Programming and Affine Relaxation for Promise Constraint Satisfaction Problems

Joshua Brakensiek, Venkatesan Guruswami, Marcin Wrochna, Stanislav Živný
2020 SIAM journal on computing (Print)  
This concerns a vast generalization of the CSP framework to the class of promise CSPs (PCSPs). In a PCSP, each constraint comes in two forms:"strict"" and"weak.""  ...  Building on the impetus of [1], Brakensiek and Guruswami systematically studied PCSPs under the polymorphic lens and established promising links to the universal-algebraic framework developed for CSPs  ...  We thank Libor Barto, Andrei Krokhin, and Jakub Opr\v sal for useful comments and encouragement. We also thank anonymous reviewers for many helpful comments.  ... 
doi:10.1137/20m1312745 fatcat:hd7moxv3crbkbeulczbttxv7am

Promise Constraint Satisfaction: Algebraic Structure and a Symmetric Boolean Dichotomy [article]

Joshua Brakensiek, Venkatesan Guruswami
2021 arXiv   pre-print
This paper considers a promise-problem variant of CSPs called PCSPs.  ...  as give necessary and sufficient conditions for the structure of this set of weak polymorphisms.  ...  Classification of Weak Polymorphisms of Folded, Symmetric Promise Relations Consider any family Γ of finitely many symmetric promise relations which contains the NOT relation.  ... 
arXiv:1704.01937v2 fatcat:iwsddj3pvnedrotkrksgl5l4du

Rainbow Coloring Hardness via Low Sensitivity Polymorphisms

Venkatesan Guruswami, Sai Sandeep
2020 SIAM Journal on Discrete Mathematics  
We prove that any such polymorphism f : [r] n → [q] must be C-fixing, i.e., there is a small subset S of C coordinates and a setting a ∈ [q] S such that fixing x |S = a determines the value of f (x).  ...  Given as input such a hypergraph, finding a r-rainbow coloring of it is NP-hard for all k ≥ 3 and r ≥ 2.  ...  As proved in [10, 12] , as with normal CSP, the complexity of a promise CSP is captured by its associated polymorphisms.  ... 
doi:10.1137/19m127731x fatcat:ji3puh626fb43psqamoqrhjjky

Symmetric Promise Constraint Satisfaction Problems: Beyond the Boolean Case [article]

Libor Barto, Diego Battistelli, Kevin M. Berg
2020 arXiv   pre-print
The Promise Constraint Satisfaction Problem (PCSP) is a recently introduced vast generalization of the Constraint Satisfaction Problem (CSP).  ...  by a ternary symmetric relation.  ...  ., the CSP over T 2 , is in P because the relation of T 2 can be described as {(x, y, z) ∈ {0, 1, 2} 3 : x + y + z = 1 (mod 3)}, and so CSP(T 2 ) can be efficiently solved by solving a system of linear  ... 
arXiv:2010.04623v1 fatcat:yrmqlyq36rbcpn7vsuxebfxgyy

Algebraic approach to promise constraint satisfaction [article]

Libor Barto, Jakub Bulín, Andrei Krokhin, Jakub Opršal
2019 arXiv   pre-print
A new version of the CSP, the promise CSP (PCSP) has recently been proposed, motivated by open questions about the approximability of variants of satisfiability and graph colouring.  ...  The basic algebraic approach to PCSP was initiated by Brakensiek and Guruswami, and in this paper we significantly extend it and lift it from concrete properties of polymorphisms to their abstract properties  ...  Acknowledgements We would like to thank Libor Barto, Mirek Olšák, Alex Kazda, Josh Brakensiek, Venkat Guruswami, Erkko Lehtonen, and Marcello Mamino for valuable discussions.  ... 
arXiv:1811.00970v3 fatcat:r2pgvc74ffcxzec6fqdkwvznm4

The Complexity of Constraint Languages [chapter]

David Cohen, Peter Jeavons
2006 Foundations of Artificial Intelligence  
Any relation from Γ LIN , and therefore any instance of CSP(Γ LIN ), can be represented by a system of linear equations 1 over D, and so can be solved in polynomial time (e.g., by Gaussian elimination)  ...  In addition, a number of novel efficient algorithms have been developed for solving particular types of constraint problems over both finite and infinite domains [3, 8, 16, 25, 26, 28, 63] .  ...  Towards a complete classification of complexity We have seen that the polymorphisms of a constraint language can identify many different tractable cases and suggest an appropriate efficient solution algorithm  ... 
doi:10.1016/s1574-6526(06)80012-x fatcat:ddy7y6xwknhjvbsnblkonm6iku

Complexity of Constraint Languages [chapter]

2013 Qualitative Spatial and Temporal Reasoning  
Any relation from Γ LIN , and therefore any instance of CSP(Γ LIN ), can be represented by a system of linear equations 1 over D, and so can be solved in polynomial time (e.g., by Gaussian elimination)  ...  In addition, a number of novel efficient algorithms have been developed for solving particular types of constraint problems over both finite and infinite domains [3, 8, 16, 25, 26, 28, 63] .  ...  Towards a complete classification of complexity We have seen that the polymorphisms of a constraint language can identify many different tractable cases and suggest an appropriate efficient solution algorithm  ... 
doi:10.1002/9781118601457.ch12 fatcat:7j7hws3cuvflnc7kn5svtfpmqe

Is the equilibrium composition of mechanochemical reactions predictable using computational chemistry?

Peter J. Bygrave, David H. Case, Graeme M. Day
2014 Faraday discussions  
Prediction of the overall reaction energies proves challenging for current methods, but the results show promise as a base on which to build more accurate and reliable approaches.  ...  The ability of computational methods to predict the structures and energetics that determine the equilibrium of solid state mechanochemical reactions has been assessed.  ...  The development of CSP methods in the past few years has been promising, with reports of successful applications to a range of challenging, exible organic molecules.  ... 
doi:10.1039/c3fd00162h pmid:25408946 fatcat:4wq3uh3lrjcrrpxmbei5c6vcmm

Quantaloidal approach to constraint satisfaction [article]

Soichiro Fujii and Yuni Iwamasa and Kei Kimura
2021 arXiv   pre-print
This observation suggests a formal development of generalisations of the CSP and concomitant notions of polymorphism in a large class of quantaloids.  ...  We point out that fundamental concepts of the CSP, such as the solution set of an instance and polymorphisms, can be formulated abstractly inside the 2-category 𝒫𝐅𝐢𝐧𝐒𝐞𝐭 of finite sets and sets of  ...  We cite [23] as a recent paper applying categorical ideas to a generalisation of the CSP called the promise CSP, although its approach and goal are entirely different from ours.  ... 
arXiv:2107.01778v1 fatcat:plolpieuwrgv3njrhgpoxlart4

Constraint Satisfaction Problems over Finite Structures [article]

Libor Barto and William DeMeo and Antoine Mottet
2021 arXiv   pre-print
We initiate a systematic study of the computational complexity of the Constraint Satisfaction Problem (CSP) over finite structures that may contain both relations and operations.  ...  In particular, we show that every finite equationally nontrivial algebra has this property which gives us, as a simple consequence, a complete complexity classification of CSPs over two-element structures  ...  non-Boolean domains and which were important for further generalizations to, e.g., infinite domains [9] , promise CSPs [1, 10, 15] , and valued CSPs [16] .  ... 
arXiv:2010.04958v2 fatcat:osswdtu2zrbatjkodmvw4dyg74
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