Almost-Symmetry in Search

Identifying and using a greater variety of symmetries often improves computational efficiency. Hence, it is natural to relax the notion of symmetry and deal with almost-symmetries which retain useful properties, occur more often and may have greater impact. In this work we consider a class of almost-symmetries, their representation, discovery and usage. Our approach is to relax the notion of graph symmetries (automorphisms) to account for vertices whose colors may change and whose edges may appear or disappear. In particular, our algorithms can discover a small number edge additions or removals that can make a given graph more symmetric.