  Effective search for graph automorphisms allows identifying symmetries in
many discrete structures, ranging from chemical molecules to microprocessor
circuits. Using this type of structure can enhance visualization as well as
speed up computational optimization and verification. Competitive algorithms
for the graph automorphism problem are based on efficient partition refinement
augmented with group-theoretic pruning techniques. In this paper, we improve
prior algorithms for the graph automorphism problem by introducing simultaneous
refinement of multiple partitions, which enables the anticipation of future
conflicts in search and leads to significant pruning, reducing overall
runtimes. Empirically, we observe an exponential speedup for the family of
Miyazaki graphs, which have been shown to impede leading graph-automorphism
algorithms.
