Mathematical Programming Computation, Volume 10, Issue 2, June 2018

Detecting almost symmetries of graphs

Ben Knueven, Jim Ostrowski, Sebastian Pokutta

We present a branch-and-bound framework to solve the following problem: Given a graph G and an integer k, find a subgraph of G formed by removing no more than k edges that minimizes the number of vertex orbits. We call the symmetries on such a subgraph “almost symmetries” of G. We implement our branch-and-bound framework in PEBBL to allow for parallel enumeration and demonstrate good scaling up to 16 cores. We show that the presented branching strategy is much better than a random branching strategy on the tested graphs. Finally, we consider the presented strategy as a heuristic for quickly finding almost symmetries of a graph G. The software that was reviewed as part of this submission has been issued the Digital Object Identifier DOI:10.5281/zenodo.840558.

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