Solution space structure of random constraint satisfaction problems with growing domains

Abstract

In this paper we study the solution space structure of model RB, a standard prototype of Constraint Satisfaction Problem (CSPs) with growing domains. Using rigorous the first and the second moment method, we show that in the solvable phase close to the satisfiability transition, solutions are clustered into exponential number of well-separated clusters, with each cluster contains sub-exponential number of solutions. As a consequence, the system has a clustering (dynamical) transition but no condensation transition. This picture of phase diagram is different from other classic random CSPs with fixed domain size, such as random K-Satisfiability (K-SAT) and graph coloring problems, where condensation transition exists and is distinct from satisfiability transition. Our result verifies the non-rigorous results obtained using cavity method from spin glass theory, and sheds light on the structures of solution spaces of problems with a large number of states.

8 pages, 1 figures

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• Gibbs States and the Set of Solutions of Random Constraint Satisfaction Problems
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Cited by in corpus (6)

• Solution space structure of random constraint satisfaction problems with growing domains
• The solution space structure of planted constraint satisfaction problems with growing domains
• SAT Requires Exhaustive Search
• Hiding solutions in model RB: Forced instances are almost as hard as unforced ones
• Exact Phase Transitions of Model RB with Slower-Growing Domains
• Super Solutions of the Model RB