The satisfiability threshold for randomly generated binary constraint satisfaction problems

Authors:
Alan Frieze;Michael Molloy
Affiliations:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh PA 15213, USA (This research was carried out during a visit to the Microsoft Research, Theory Group);Department of Computer Science, University of Toronto, Toronto, Ontario M5S 3G4, Canada (This research was carried out while he was a Visiting Researcher at Microsoft Research)
Venue:
Random Structures & Algorithms
Year:
2006

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Abstract

We study two natural models of randomly generated constraint satisfaction problems. We determine how quickly the domain size must grow with n to ensure that these models are robust in the sense that they exhibit a non-trivial threshold of satisfiability, and we determine the asymptotic order of that threshold. We also provide resolution complexity lower bounds for these models. One of our results immediately yields a theorem regarding homomorphisms between two random graphs. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2006