Isomorphism Checking in GROOVE

Arend Rensink

Abstract


In this paper we show how isomorphism checking can be used as an effective technique for symmetry reduction in graph-based state spaces, despite the inherent complexity of the isomorphism problem. In particular, we show how one can use /element-based graph certificate mappings/ to help in recognising non-isomorphic graphs. These are mappings that assign to all elements (edges and nodes) of a given graph a number that is invariant under isomorphism, in the sense that any isomorphism between graphs is sure to preserve this number. The individual element certificates of a graph give rise to a certificate for the entire graph, which can be used as a hash key for the graph; hence, this yields a heuristic to decide whether a graph has an isomorphic representative in a previously computed set of graphs. We report some experiments that show the viability of this method.

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DOI: http://dx.doi.org/10.14279/tuj.eceasst.1.77

DOI (PDF): http://dx.doi.org/10.14279/tuj.eceasst.1.77.84

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