Towards breaking more composition symmetries in partial symmetry breaking

Abstract

The paper proposes a dynamic method, Recursive Symmetry Breaking During Search (ReSBDS), for efficient partial symmetry breaking. We first demonstrate how Partial Symmetry Breaking During Search (ParSBDS) misses important pruning opportunities when given only a subset of symmetries to break. The investigation pinpoints the culprit and in turn suggests rectification. The main idea is to add extra symmetry breaking constraints during search recursively to prune also symmetric nodes of some pruned subtrees. Thus, ReSBDS can break extra symmetry compositions, but is carefully designed to break only the ones that are easy to identify and inexpensive to break. We present theorems to guarantee the soundness and termination of our approach, and compare our method with popular static and dynamic methods. When the variable (value) heuristic is static, ReSBDS is also complete in eliminating all interchangeable variables (values) given only the generator symmetries. We propose further a light version of ReSBDS method (LReSBDS), which has a slightly weaker pruning power of ReSBDS but with a reduced overhead. We give theoretical characterization on the soundness and termination of LReSBDS, and comparisons on pruning strengths against other symmetry breaking methods including ReSBDS. Extensive experimentations confirm the efficiency of ReSBDS and LReSBDS, when compared against state of the art methods.