Accelerating Random Walks

Abstract

In recent years, there has been much research on local search techniques for solving constraint satisfaction problems, including Boolean satisfiability problems. Some of the most successful procedures combine a form of random walk with a greedy bias. These procedures are quite effective in a number of problem domains, for example, constraint-based planning and scheduling, graph coloring, and hard random problem instances. However, in other structured domains, backtrack-style procedures are often more effective. We introduce a technique that leads to significant speedups of random walk style procedures on structured problem domains. Our method identifies long range dependencies among variables in the underlying problem instance. Such dependencies are made explicit by adding new problem constraints. These new constraints can be derived efficiently, and, literally, “accelerate” the Random Walk search process. We provide a formal analysis of our approach and an empirical validation on a recent benchmark collection of hardware verification problems.