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@james-d-mitchell james-d-mitchell released this 08 Jun 18:26
· 1099 commits to main since this release
v0.5.1
cbb3c61

This release contains some bugfixes, some minor new features, and some performance improvements. The package has moved to GitHub and we welcome Finn Smith as an author.

This release contains a new technique for encoding a vertex-coloured digraph as a vertex-coloured (undirected) graph while preserving the automorphism group, in order to calculate the automorphism group using bliss. These changes were made by Finn Smith. The previous technique involved adding two intermediate vertices for every edge; on a digraph with n vertices this could add 2n(n-1) new vertices. The new technique encodes a digraph with n vertices as a graph with 3n vertices. In certain cases, this can lead to a dramatic improvement in the time taken to calculate the automorphism group.

The new reduction is based on two techniques in:

David Bremner, Mathieu Dutour Sikiric, Dmitrii V. Pasechnik, Thomas Rehn, Achill Schürmann. Computing symmetry groups of polyhedra. https://arxiv.org/abs/1210.0206v3

Namely, "Dealing with digraphs" followed by "Reduction by superposition". From the graph obtained by these techniques, n vertices which are irrelevant to automorphism finding are removed.

The actual reduction used is as follows: Given a digraph D=(V=[]1 .. n],E,c), create three copies V1, V2, V3 of the vertex set V. Colour V1 according to the colouring c of D, and V2, V3 with two distinct colours that do not occur in D. Connect each vertex in V1 to the corresponding vertices in V2, V3. For every arc (x,y) in E, put an edge between the copy of x in V2, and the copy of y in V3. Automorphisms of this graph, when restricted to V, are precisely the automorphisms of D. Because this changes the graph used to calculate automorphisms, the results sometimes nominally differ from the previous version - especially in the case of canonical labelling, where unrecognisably different results may appear. Generators also often appear in different orders.

The performance improvements are most noticeable on large, quite dense digraphs. On random digraphs with 5000 vertices and 0.5 edge probability, 200-400x speedups were common. When calculating the automorphism group of the complete digraph on 1000 vertices, with vertex i having colour i mod 2 + 1, we obtain a 66x speedup. When the vertex i is assigned colour i mod 7 + 1, this becomes a 400x speedup.

Minor changes include:

  • a better method for DigraphReverse [Wilf Wilson]
  • automorphism groups of complete, empty, cycle, chain, and complete bipartite digraphs are set at creation Michael Torpey
  • a minor improvement in performance in the DigraphMaximalCliques [Wilf Wilson]
  • a new operation AdjacencyMatrixMutableCopy [James D. Mitchell]
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