Trail Saving on Backtrack

Abstract

A CDCL SAT solver can backtrack a large distance when it learns a new clause, e.g, when the new learnt clause is a unit clause the solver has to backtrack to level zero. When the length of the backtrack is large, the solver can end up reproducing many of the same decisions and propagations when it redescends the search tree. Different techniques have been proposed to reduce this potential redundancy, e.g., partial/chronological backtracking and trail saving on restarts. In this paper we present a new trail saving technique that is not restricted to restarts, unlike prior trail saving methods. Our technique makes a copy of the part of the trail that is backtracked over. This saved copy can then be used to improve the efficiency of the solver’s subsequent redescent. Furthermore, the saved trail also provides the solver with the ability to look ahead along the previous trail which can be exploited to improve its efficiency. Our new trail saving technique offers different tradeoffs in comparison with chronological backtracking and often yields superior performance. We also show that our technique is able to improve the performance of state-of-the-art solvers.