Faster symmetry discovery using sparsity of symmetries

Many computational tools have recently begun to benefit from the use of the symmetry inherent in the tasks they solve, and use general-purpose graph symmetry tools to uncover this symmetry. However, existing tools suffer quadratic runtime in the number of symmetries explicitly returned and are of limited use on very large, sparse, symmetric graphs. This paper introduces a new symmetry-discovery algorithm which exploits the sparsity present not only in the input but also the output, i.e., the symmetries themselves. By avoiding quadratic runtime on large graphs, it improves state-of- the-art runtimes from several days to less than a second.