Affiliation:
1. Universidad del País Vasco and IKERBASQUE, Basque Foundation for Science, Spain
2. Champlain Regional College and Université du Québec a Montréal
Abstract
The constraint satisfaction problem (CSP) involves deciding, given a set of variables and a set of constraints on the variables, whether or not there is an assignment to the variables satisfying all of the constraints. One formulation of the CSP is as the problem of deciding, given a pair (G ℍ) of relational structures, whether or not there is a homomorphism from the first structure to the second structure. The CSP is generally NP-hard; a common way to restrict this problem is to fix the second structure ℍ so that each structure ℍ gives rise to a problem CSP(ℍ). The problem family CSP(ℍ) has been studied using an algebraic approach, which links the algorithmic and complexity properties of each problem CSP(ℍ) to a set of operations, the so-called polymorphisms of ℍ. Certain types of polymorphisms are known to imply the polynomial-time tractability of CSP(ℍ), and others are conjectured to do so. This article systematically studies—for various classes of polymorphisms—the computational complexity of deciding whether or not a given structure ℍ admits a polymorphism from the class. Among other results, we prove the NP-completeness of deciding a condition conjectured to characterize the tractable problems CSP(ℍ), as well as the NP-completeness of deciding if CSP(ℍ) has bounded width.
Funder
Spanish Project MINECO COMMAS
Basque
FRQNT and NSERC
Basque Project
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Theory and Mathematics,Theoretical Computer Science
Cited by
12 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献