Affiliation:
1. Simon Fraser University, British Columbia, Canada
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].
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Mathematics,Logic,General Computer Science,Theoretical Computer Science
Reference45 articles.
1. Polynomial interpolation and the Chinese Remainder Theorem for algebraic systems
2. Near-Unanimity Functions and Varieties of Reflexive Graphs
3. Bulatov A. 2002b. Mal'tsev constraints are tractable. Tech. rep. PRG-RR-02-05. Computing Laboratory University of Oxford Oxford U.K. Bulatov A. 2002b. Mal'tsev constraints are tractable. Tech. rep. PRG-RR-02-05. Computing Laboratory University of Oxford Oxford U.K.
4. Combinatorial problems raised from 2-semilattices
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