Approximate Inference for Clusters in Solution Spaces

Lukas Kroc, Ashish Sabharwal, Bart Selman

Abstract: This work proposes new approximate (and exact) inference methods for reasoning about an important and hard-to-compute property of the solution space of combinatorial problems, namely clusters of solutions. Given a constraint satisfaction problem (CSP), we can think of two solutions as being "connected" if they differ in the value of only one variable. Clusters of solutions can thus be defined in a natural manner: two solutions s1 and s2 are in the same cluster if and only if there is a path of connected solutions from s1 to s2. The main question we seek to address is, given a CSP, how many solution clusters does it have?.