The complexity of temporal constraint satisfaction problems

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 be useful in similar contexts of constraint satisfaction complexity classification. Categories and Subject Descriptors F.2 [Theory of Computation]: Analysis of Algorithms and Problem Complexity; F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems—Computations on discrete structures General Terms Theory, Algorithms Keywords Constraint satisfa...

• Type: Journal
• Year: 2010
• Where: JACM
• Authors: Manuel Bodirsky, Jan Kára
• Keywords: Constraint Satisfaction, JACM 2010, Temporal Constraint, Temporal Constraint Languages