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Novel Techniques for Automorphism Group Computation

Lopéz-Presa, José Luis and Chiroque, Luis F. and Fernández Anta, Antonio (2013) Novel Techniques for Automorphism Group Computation. In: The 12th International Symposium on Experimental Algorithms (SEA 2013), 5 - 7 June 2013, Rome, Italy.

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Graph automorphism (GA) is a classical problem, in which the objective is to compute the automorphism group of an input graph. In this work we propose four novel techniques to speed up algorithms that solve the GA problem by exploring a search tree. They increase the performance of the algorithm by allowing to reduce the depth of the search tree, and by effectively pruning it. We formally prove that a GA algorithm that uses these techniques correctly computes the automorphism group of the input graph. We also describe how the techniques have been incorporated into the GA algorithm conauto, as conauto-2.03, with at most an additive polynomial increase in its asymptotic time complexity. We have experimentally evaluated the impact of each of the above techniques with several graph families. We have observed that each of the techniques by itself significantly reduces the number of processed nodes of the search tree in some subset of graphs, which justifies the use of each of them. Then, when they are applied together, their effect is combined, leading to reductions in the number of processed nodes in most graphs. This is also reflected in a reduction of the running time, which is substantial in some graph families.

Item Type: Conference or Workshop Papers (Paper)
Additional Information: Springer 2013 Lecture Notes in Computer Science ISBN 978-3-642-38526-1
Depositing User: Antonio Fernandez
Date Deposited: 10 Sep 2013 11:56
Last Modified: 03 Mar 2014 09:04

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