research-article

Complexity of conservative constraint satisfaction problems

Author:

Andrei A. BulatovAuthors Info & Claims

ACM Transactions on Computational Logic (TOCL), Volume 12, Issue 4

Article No.: 24, Pages 1 - 66

https://doi.org/10.1145/1970398.1970400

Published: 22 July 2011 Publication History

Abstract

In a constraint satisfaction problem (CSP), the aim is to find an assignment of values to a given set of variables, subject to specified constraints. The CSP is known to be NP-complete in general. However, certain restrictions on the form of the allowed constraints can lead to problems solvable in polynomial time. Such restrictions are usually imposed by specifying a constraint language, that is, a set of relations that are allowed to be used as constraints. A principal research direction aims to distinguish those constraint languages that give rise to tractable CSPs from those that do not.

We achieve this goal for the important version of the CSP, in which the set of values for each individual variable can be restricted arbitrarily. Restrictions of this type can be studied by considering those constraint languages which contain all possible unary constraints; we call such languages conservative. We completely characterize conservative constraint languages that give rise to polynomial time solvable CSP classes. In particular, this result allows us to obtain a complete description of those (directed) graphs H for which the List H-Coloring problem is solvable in polynomial time. The result, the solving algorithm, and the proofs heavily use the algebraic approach to CSP developed in Jeavons et al. [1997], Jeavons [1998], Bulatov et al. [2005], and Bulatov and Jeavons [2001b, 2003].

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Index Terms

Complexity of conservative constraint satisfaction problems
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
      1. Combinatorial algorithms
2. Theory of computation
  1. Computational complexity and cryptography
    1. Problems, reductions and completeness
  2. Logic
    1. Constraint and logic programming

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cover image ACM Transactions on Computational Logic

ACM Transactions on Computational Logic Volume 12, Issue 4

July 2011

295 pages

ISSN:1529-3785

EISSN:1557-945X

DOI:10.1145/1970398

Issue’s Table of Contents

Copyright © 2011 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 22 July 2011

Accepted: 01 April 2010

Revised: 01 December 2008

Received: 01 December 2003

Published in TOCL Volume 12, Issue 4

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Amezian El Khalfioui AWijsen J(2024)Computing Range Consistent Answers to Aggregation Queries via RewritingProceedings of the ACM on Management of Data10.1145/36958362:5(1-19)Online publication date: 7-Nov-2024
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Koutris POuyang XWijsen J(2024)Consistent Query Answering for Primary Keys on Rooted Tree QueriesProceedings of the ACM on Management of Data10.1145/36511392:2(1-26)Online publication date: 14-May-2024
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Focke JMarx DRzążewski P(2024)Counting List Homomorphisms from Graphs of Bounded Treewidth: Tight Complexity BoundsACM Transactions on Algorithms10.1145/364081420:2(1-32)Online publication date: 13-Feb-2024
https://dl.acm.org/doi/10.1145/3640814
Bok JBrewster RFeder THell PJedličková N(2024)List homomorphisms to separable signed graphsTheoretical Computer Science10.1016/j.tcs.2024.1145801001(114580)Online publication date: Jun-2024
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Livieratos JKolaitis PKirousis L(2022)On the Computational Complexity of Non-Dictatorial AggregationJournal of Artificial Intelligence Research10.1613/jair.1.1247672(137-183)Online publication date: 4-Jan-2022
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Carbonnel CRomero MŽivný S(2022)The Complexity of General-Valued Constraint Satisfaction Problems Seen from the Other SideSIAM Journal on Computing10.1137/19M125012151:1(19-69)Online publication date: 25-Jan-2022
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