Counting with Combined Splitting and Capture-Recapture Methods
  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. 
Paul Dupuis, Bahar Kaynar, Ad Ridder, Reuven Rubinstein, Radislav   Vaisman
stat.CO math.PR