On the connections between backdoors, restarts, and heavy-tailedness in combinatorial search

Recent state-of-the-art SAT solvers can handle hand-crafted instances with hundreds of thousands of variables and several million clauses. Only a few years ago, the ability to handle such instances appeared completely out of reach. The most effective complete solvers are generally based on DavisPutnam-Loveland-Logemann style search procedures augmented with a number of special techniques, such as clause-learning, non-chronological backtracking, lookahead, fast unit-propagation, randomization, and restart strategies. The progress in this area has largely been driven by experimental work on diverse sets of benchmark problems, including regular SAT competitions. Given the tremendous advances in recent years, this has clearly been a highly successful approach. One key open area of research is to obtain a better understanding as to why these methods work so well. In this paper, we hope to advance our understanding of the effectiveness of current techniques and analyze what features of practical instances makes them so amenable to these solution methods. Of the many enhancements of DPLL, we will focus our attention on the interplay between certain special features of problem instances, polytime propagation methods, and restart techniques. This analysis is clearly only part of the full story, since other enhancements, such as clause learning and non-chronological backtracking, provide additional power to these solvers.