Breaking symmetries in graphs: The nauty way

Abstract

Symmetry breaking is an essential component when solving graph search problems as it restricts the search space to that of canonical representations. There are an abundance of powerful tools, such as nauty, which apply to find the canonical representation of a given graph and to test for isomorphisms given a set of graphs. In contrast, for graph search problems, current symmetry breaking techniques are partial and solvers unnecessarily explore an abundance of isomorphic parts of the search space. This paper is novel in that it introduces complete symmetry breaking for graph search problems by modeling, in terms of constraints, the same ideas underlying the algorithm applied in tools like nauty. Whereas nauty tests given graphs, symmetry breaks restrict the search space and apply during generation.