BFS Enumeration for Breaking Symmetries in Graphs

TL;DR

This paper introduces three new symmetry-breaking predicates for BFS-based graph enumeration to reduce search space and improve efficiency in solving NP-hard graph problems, demonstrating practical effectiveness.

Contribution

The paper presents novel BFS-based symmetry-breaking predicates and compares their performance with existing methods on various graph problems.

Findings

New predicates reduce search space effectively

Improved solving speed over existing methods

Validated on multiple graph problem instances

Abstract

There are numerous NP-hard combinatorial problems which involve searching for an undirected graph satisfying a certain property. One way to solve such problems is to translate a problem into an instance of the boolean satisfiability (SAT) or constraint satisfaction (CSP) problem. Such reduction usually can give rise to numerous isomorphic representations of the same graph. One way to reduce the search space and speed up the search under these conditions is to introduce symmetrybreaking predicates. In this paper we introduce three novel and practically effective symmetry-breaking predicates for an undirected connected graph search based on breadth-first search (BFS) enumeration and compare with existing symmetry-breaking methods on several graph problems.