Formal Models of Heavy-Tailed Behavior in Combinatorial Search

Contents

Recently, it has been found that the cost distributions of randomized backtrack search in combinatorial domains are often heavytailed. Such heavy-tailed distributions explain the high variability observed when using backtrack-style procedures. A good understanding of this phenomenon can lead to better search techniques. For example, restart strategies provide a good mechanism for eliminating the heavytailed behavior and boosting the overall search performance. Several state-of-the-art SAT solvers now incorporate such restart mechanisms. The study of heavy-tailed phenomena in combinatorial search has so far been been largely based on empirical data. We introduce several abstract tree search models, and show formally how heavy-tailed cost distribution can arise in backtrack search. We also discuss how these insights may facilitate the development of better combinatorial search methods.