SCS

Abstract

We present a new method for rare-event probability estimation, combinatorial optimization and counting, called the stochastic enumeration (SE) method. In terms of counting, SE presents a stochastic replica of the naive full enumeration method. It is well known that the latter is typically meaningless since the associated counting sets, such as the sets of feasible solutions of the integer programming constraints, are huge. The SE method overcomes this difficulty by using a manageable sample size. We show how to implement the SE method for some well known difficult counting problems, such as self-avoiding walks, 0-1 tables and satisfiability problems, discuss its convergence, and present numerical studies demonstrating its superiority to the classic splitting method.