Local Search and the Number of Solutions

There has been considerable research interest into the solubility phase transition, and its effect on search cost for backtracking algorithms. In this paper we show that a similar easy-hard-easy pattern occurs for local search, with search cost peaking at the phase transition. This is despite problems beyond the phase transition having fewer solutions, which intuitively should make the problems harder to solve. We examine the relationship between search cost and number of solutions at different points across the phase transition, for three different local search procedures, across two problem classes (CSP and SAT). Our findings show that there is a significant correlation, which changes as we move through the phase transition.

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