Counting with Combined Splitting and Capture-Recapture Methods

TL;DR

This paper introduces an improved splitting method combined with capture-recapture techniques to efficiently estimate solutions for complex counting problems like 3-SAT, random graphs, and contingency tables, demonstrating superior performance in experiments.

Contribution

It presents an enhanced splitting method integrating capture-recapture, showing improved variance reduction and speed for counting problems compared to existing approaches.

Findings

Capture-recapture method reduces estimator variance

Enhanced method outperforms traditional splitting in speed

Effective for complex combinatorial counting problems

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.