research-article

Constraint Satisfaction Problems Solvable by Local Consistency Methods

Authors:

Marcin KozikAuthors Info & Claims

Journal of the ACM (JACM), Volume 61, Issue 1

Article No.: 3, Pages 1 - 19

https://doi.org/10.1145/2556646

Published: 01 January 2014 Publication History

Abstract

We prove that constraint satisfaction problems without the ability to count are solvable by the local consistency checking algorithm. This settles three (equivalent) conjectures: Feder--Vardi [SICOMP’98], Bulatov [LICS’04] and Larose--Zádori [AU’07].

References

[1]

Libor Barto. 2013. The collapse of the bounded width hierarchy. In preparation.

[2]

Libor Barto and Marcin Kozik. 2009a. Congruence distributivity implies bounded width. SIAM J. Comput. 39, 4, 1531--1542.

Digital Library

[3]

Libor Barto and Marcin Kozik. 2009b. Constraint satisfaction problems of bounded width. In Proceedings of the 50th Symposium on Foundations of Computer Science (FOCS’09). 595--603.

Digital Library

[4]

Libor Barto and Marcin Kozik. 2010. New conditions for Taylor varieties and CSP. In Proceedings of the 25th Annual IEEE Symposium on Logic in Computer Science (LICS’10). IEEE Computer Society, Los Alamitos, CA, 100--109.

Digital Library

[5]

Libor Barto and Marcin Kozik. 2012. Robust satisfiability of constraint satisfaction problems. In Proceedings of the 44th Symposium on Theory of Computing (STOC’12). ACM, New York, 931--940.

Digital Library

[6]

Libor Barto, Marcin Kozik, and David Stanovský. 2013. Mal’tsev conditions, lack of absorption, and solvability. Submitted.

[7]

C. Bergman. 2011. Universal Algebra: Fundamentals and Selected Topics. Taylor and Francis. http://books.google.ca/books?id=QXi3BZWoMRwC.

[8]

Joel Berman, Pawel Idziak, Petar Marković, Ralph McKenzie, Matthew Valeriote, and Ross Willard. 2009. Varieties with few subalgebras of powers. Trans. Amer. Math. Soc. 362, 1445--1473.

[9]

Garrett Birkhoff. 1935. On the structure of abstract algebras. Proc. Cambridge Philos. Soc. 31, 433--454.

[10]

V. G. Bodnarčuk, L. A. Kalužnin, V. N. Kotov, and B. A. Romov. 1969. Galois theory for Post algebras. I, II. Kibernetika (Kiev) 3, 1--10; ibid. 1969, no. 5, 1--9.

[11]

Andrei Bulatov. 2006a. Complexity of Maltsev constraints. Algebra i Logika 26, 1, (In Russian).

[12]

Andrei Bulatov. 2009. Bounded relational width. Manuscript. http://www.cs.sfu.ca/~abulatov/papers/relwidth.pdf.

[13]

Andrei Bulatov and Víctor Dalmau. 2006. A simple algorithm for Mal′tsev constraints. SIAM J. Comput. 36, 1, 16--27 (electronic).

Digital Library

[14]

Andrei Bulatov, Peter Jeavons, and Andrei Krokhin. 2005. Classifying the complexity of constraints using finite algebras. SIAM J. Comput. 34, 720--742. Issue 3.

Digital Library

[15]

Andrei A. Bulatov. 2003. Tractable conservative constraint satisfaction problems. In Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science. IEEE Computer Society, Los Alamitos, CA, 321--.

Digital Library

[16]

A. A. Bulatov. 2004a. Complexity of the conservative generalized satisfiability problem. Dokl. Akad. Nauk 397, 5, 583--585.

[17]

Andrei A. Bulatov. 2004b. A graph of a relational structure and constraint satisfaction problems. In Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science (LICS’04). IEEE Computer Society Press, Los Alamitos, CA, 448--457.

Digital Library

[18]

Andrei A. Bulatov. 2006b. Combinatorial problems raised from 2-semilattices. J. Algebra 298, 2, 321--339.

[19]

Andrei A. Bulatov. 2006c. A dichotomy theorem for constraint satisfaction problems on a 3-element set. J. ACM 53, 1, 66--120.

Digital Library

[20]

Andrei A. Bulatov and Matthew Valeriote. 2008. Recent results on the algebraic approach to the CSP. In Complexity of Constraints, Nadia Creignou, Phokion G. Kolaitis, and Heribert Vollmer Eds., Lecture Notes in Computer Science, vol. 5250, Springer, 68--92. http://dblp.uni-trier.de/db/conf/dagstuhl/coc2008.html#BulatovV08.

Digital Library

[21]

Andrei A. Bulatov, Andrei A. Krokhin, and Peter Jeavons. 2000. Constraint satisfaction problems and finite algebras. In Automata, Languages and Programming. Lecture Notes in Computer Science, vol. 1853, Springer, Berlin, 272--282.

Digital Library

[22]

Andrei A. Bulatov, Andrei Krokhin, and Benoit Larose. 2008. Dualities for constraint satisfaction problems. In Complexity of Constraints, Springer-Verlag, Berlin, 93--124.

Digital Library

[23]

Stanley N. Burris and H. P. Sankappanavar. 1981. A Course in Universal Algebra. Graduate Texts in Mathematics, Vol. 78, Springer-Verlag, New York.

[24]

Catarina Carvalho, Víctor Dalmau, Petar Marković, and Miklós Maróti. 2009. CD(4) has bounded width. Algebra Universalis 60, 3, 293--307.

[25]

Tomás Feder and Moshe Y. Vardi. 1998. The computational structure of monotone monadic SNP and constraint satisfaction: A study through datalog and group theory. SIAM J. Comput. 28, 1, 57--104.

Digital Library

[26]

David Geiger. 1968. Closed systems of functions and predicates. Pacific J. Math. 27, 95--100.

[27]

David Hobby and Ralph McKenzie. 1988. The Structure of Finite Algebras. Contemporary Mathematics, Vol. 76, American Mathematical Society, Providence, RI.

[28]

Pawel Idziak, Petar Marković, Ralph McKenzie, Matthew Valeriote, and Ross Willard. 2007. Tractability and learnability arising from algebras with few subpowers. In Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science (LICS’07). IEEE Computer Society Press, Los Alamitos, CA, 213--222.

Digital Library

[29]

Peter Jeavons, David Cohen, and Marc Gyssens. 1997. Closure properties of constraints. J. ACM 44, 4, 527--548.

Digital Library

[30]

Emil Kiss and Matthew Valeriote. 2007. On tractability and congruence distributivity. Log. Meth. Comput. Sci. 3, 2, 2:6, (electronic).

[31]

Benoît Larose and Pascal Tesson. 2009. Universal algebra and hardness results for constraint satisfaction problems. Theoret. Comput. Sci. 410, 18, 1629--1647.

Digital Library

[32]

Benoît Larose and László Zádori. 2007. Bounded width problems and algebras. Algebra Universalis 56, 3--4, 439--466.

[33]

Benoît Larose, Matt Valeriote, and László Zádori. 2009. Omitting types, bounded width and the ability to count. Internat. J. Algebra Comput. 19, 5, 647--668.

[34]

Miklós Maróti and Ralph McKenzie. 2008. Existence theorems for weakly symmetric operations. Algebra Universalis 59, 3--4, 463--489.

Cited By

Mottet APinsker M(2024)Smooth approximations: An algebraic approach to CSPs over finitely bounded homogeneous structuresJournal of the ACM10.1145/368920771:5(1-47)Online publication date: 17-Aug-2024
https://dl.acm.org/doi/10.1145/3689207
Ciardo LSobocinski PLago UEsparza J(2024)Quantum advantage and CSP complexityProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662118(1-15)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3661814.3662118
Barto LButti SKazda AViola CŽivný SSobocinski PLago UEsparza J(2024)Algebraic Approach to ApproximationProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662076(1-14)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3661814.3662076
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Index Terms

Constraint Satisfaction Problems Solvable by Local Consistency Methods
1. Theory of computation

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cover image Journal of the ACM

Journal of the ACM Volume 61, Issue 1

January 2014

222 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/2578041

Editor:
Victor Vianu
University of California, San Diego

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Copyright © 2014 ACM.

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Association for Computing Machinery

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Publication History

Published: 01 January 2014

Accepted: 01 November 2013

Revised: 01 February 2013

Received: 01 March 2012

Published in JACM Volume 61, Issue 1

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Cited By

Mottet APinsker M(2024)Smooth approximations: An algebraic approach to CSPs over finitely bounded homogeneous structuresJournal of the ACM10.1145/368920771:5(1-47)Online publication date: 17-Aug-2024
https://dl.acm.org/doi/10.1145/3689207
Ciardo LSobocinski PLago UEsparza J(2024)Quantum advantage and CSP complexityProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662118(1-15)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3661814.3662118
Barto LButti SKazda AViola CŽivný SSobocinski PLago UEsparza J(2024)Algebraic Approach to ApproximationProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662076(1-14)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3661814.3662076
Dalmau VOpršal JSobocinski PLago UEsparza J(2024)Local consistency as a reduction between constraint satisfaction problemsProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662068(1-15)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3661814.3662068
Bodirsky MBodor B(2024)A Complexity Dichotomy in Spatial Reasoning via Ramsey TheoryACM Transactions on Computation Theory10.1145/364944516:2(1-39)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3649445
Bulatov A(2024)Graphs of finite algebras: edges, and connectivityAlgebra universalis10.1007/s00012-024-00865-585:4Online publication date: 30-Oct-2024
https://doi.org/10.1007/s00012-024-00865-5
Prokic ADjapic PMarkovic PMcKenzie R(2023)SMB algebras I: On the variety of SMB algebrasFilomat10.2298/FIL2313083P37:13(4083-4101)Online publication date: 2023
https://doi.org/10.2298/FIL2313083P
Brakensiek JGuruswami VSandeep SSaha BServedio R(2023)SDPs and Robust Satisfiability of Promise CSPProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585180(609-622)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585180
Ciardo LŽivný SSaha BServedio R(2023)Approximate Graph Colouring and the Hollow ShadowProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585112(623-631)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585112
Ciardo LŽivný S(2023)CLAP: A New Algorithm for Promise CSPsSIAM Journal on Computing10.1137/22M147643552:1(1-37)Online publication date: 25-Jan-2023
https://doi.org/10.1137/22M1476435
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