Linear satisfiability preserving assignments

Kei Kimura, Kazuhisa Makino

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we study several classes of satisfiability preserving assignments to the constraint satisfaction problem. In particular, we consider fixable, autark and satisfying assignments. Since it is in general NP-hard to find a nontrivial (i.e., nonempty) satisfiability preserving assignment, we introduce linear satisfiability preserving assignments, which are defined by polyhedral cones in an associated vector space. The vector space is obtained by the identification, introduced by Kullmann, of assignments with real vectors. We consider arbitrary polyhedral cones, where only restricted classes of cones for autark assignments are considered in the literature. We reveal that cones in certain classes are maximal as a convex subset of the set of the associated vectors, which can be regarded as extensions of Kullmann's results for autark assignments of CNFs. As algorithmic results, we present a pseudo-polynomial time algorithm that computes a linear fixable assignment for a given integer linear system, which implies the well known pseudo-polynomial solvability for integer linear systems such as two-variable-per-inequality, Horn and q-Horn systems.

Original languageEnglish
Title of host publicationProceedings of the 27th International Joint Conference on Artificial Intelligence, IJCAI 2018
EditorsJerome Lang
PublisherInternational Joint Conferences on Artificial Intelligence
Pages5622-5626
Number of pages5
ISBN (Electronic)9780999241127
Publication statusPublished - 2018
Externally publishedYes
Event27th International Joint Conference on Artificial Intelligence, IJCAI 2018 - Stockholm, Sweden
Duration: Jul 13 2018Jul 19 2018

Publication series

NameIJCAI International Joint Conference on Artificial Intelligence
Volume2018-July
ISSN (Print)1045-0823

Other

Other27th International Joint Conference on Artificial Intelligence, IJCAI 2018
Country/TerritorySweden
CityStockholm
Period7/13/187/19/18

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence

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