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* Some further minor performance improvements were made and a compiler warning
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was fixed.
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* Some further minor performance improvements were made, and a compiler warning
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was fixed.
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## Version 1.0.3 (released 29/11/2019)
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@@ -578,14 +579,14 @@ Smith as an author.
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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.
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The new reduction is based on two techniques in:
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The new reduction is based on two techniques in:
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> David Bremner, Mathieu Dutour Sikiric, Dmitrii V. Pasechnik, Thomas Rehn, Achill Schürmann. Computing symmetry groups of polyhedra. https://arxiv.org/abs/1210.0206v3
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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.
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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`.
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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.
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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`.
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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.
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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.
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