The time complexity of constraint satisfaction

Authors:
Patrick Traxler
Affiliations:
Institute of Theoretical Computer Science, ETH Zürich, Switzerland
Venue:
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Year:
2008

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Abstract

We study the time complexity of (d, k)-CSP, the problem ofdeciding satisfiability of a constraint system C with n variables, domainsize d, and at most k variables per constraint. We are interested in thequestion how the domain size d influences the complexity of decidingsatisfiability. We show, assuming the Exponential Time Hypothesis, thattwo special cases, namely (d, 2)-CSP with bounded variable frequencyand d-UNIQUE-CSP, already require exponential time Ω(dcċn) for somec 0 independent of d. UNIQUE-CSP is the special case for which it isguaranteed that every input constraint system has at most 1 satisfyingassignment.