Counting with Combined Splitting and Capture-Recapture Methods

Abstract: We apply the splitting method to three well-known counting problems, namely 3-SAT, random graphs with prescribed degrees, and binary contingency tables. We present an enhanced version of the splitting method based on the capture-recapture technique, and show by experiments the superiority of this technique for SAT problems in terms of variance of the associated estimators, and speed of the algorithms.