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The complexity of temporal constraint satisfaction problems

Published: 08 February 2010 Publication History

Abstract

A temporal constraint language is a set of relations that has a first-order definition in(Q;<), the dense linear order of the rational numbers. We present a complete complexity classification of the constraint satisfaction problem (CSP) for temporal constraint languages: if the constraint language is contained in one out of nine temporal constraint languages, then the CSP can be solved in polynomial time; otherwise, the CSP is NP-complete. Our proof combines model-theoretic concepts with techniques from universal algebra, and also applies the so-called product Ramsey theorem, which we believe will useful in similar contexts of constraint satisfaction complexity classification.
An extended abstract of this article appeared in the proceedings of STOC'08.

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cover image Journal of the ACM
Journal of the ACM  Volume 57, Issue 2
January 2010
248 pages
ISSN:0004-5411
EISSN:1557-735X
DOI:10.1145/1667053
Issue’s Table of Contents
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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Association for Computing Machinery

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Publication History

Published: 08 February 2010
Accepted: 01 September 2009
Revised: 01 September 2009
Received: 01 August 2008
Published in JACM Volume 57, Issue 2

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Author Tags

  1. Logic
  2. algorithms
  3. complexity
  4. constraints

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  • (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
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