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Theory of Computing Systems

, Volume 48, Issue 3, pp 444–464 | Cite as

Tractable Structures for Constraint Satisfaction with Truth Tables

  • Dániel Marx
Article

Abstract

The way the graph structure of the constraints influences the complexity of constraint satisfaction problems (CSP) is well understood for bounded-arity constraints. The situation is less clear if there is no bound on the arities. In this case the answer depends also on how the constraints are represented in the input. We study this question for the truth table representation of constraints. We introduce a new hypergraph measure adaptive width and show that CSP with truth tables is polynomial-time solvable if restricted to a class of hypergraphs with bounded adaptive width. Conversely, assuming a conjecture on the complexity of binary CSP, there is no other polynomial-time solvable case. Finally, we present a class of hypergraphs with bounded adaptive width and unbounded fractional hypertree width.

Computational complexity Constraint satisfaction Treewidth Adaptive width 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Tel Aviv UniversityTel AvivIsrael

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