Novel Techniques to Speed Up the Computation of the Automorphism Group of a Graph
Graph automorphism (GA) is a classical problem, in which the objective is to compute the automorphism group of an input graph. Most GA algorithms explore a search tree using the individualization-refinement procedure. Four novel techniques are proposed which increase the performance of any algorithm...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/934637 |
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| _version_ | 1832559043266215936 |
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| author | José Luis López-Presa Luis F. Chiroque Antonio Fernández Anta |
| author_facet | José Luis López-Presa Luis F. Chiroque Antonio Fernández Anta |
| author_sort | José Luis López-Presa |
| collection | DOAJ |
| description | Graph automorphism (GA) is a classical problem, in which the objective is to compute the automorphism group of an input graph. Most GA algorithms explore a search tree using the individualization-refinement procedure. Four novel techniques are proposed which increase the performance of any algorithm of this type by reducing 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 an input graph. Then, we describe how these 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. Using a benchmark of different graph families, we have evaluated the impact of these techniques on the size of the search tree, observing a significant reduction both when they are applied individually and when all of them are applied together. This is also reflected in a reduction of the running time, which is substantial for some graph families. Finally, we have compared the search tree size of conauto-2.03 against those of other popular GA algorithms, observing that, in most cases, conauto explores less nodes than these algorithms. |
| format | Article |
| id | doaj-art-f6a202da1e114175b3f82ef0599a172a |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-f6a202da1e114175b3f82ef0599a172a2025-02-03T01:31:07ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/934637934637Novel Techniques to Speed Up the Computation of the Automorphism Group of a GraphJosé Luis López-Presa0Luis F. Chiroque1Antonio Fernández Anta2DIATEL-UPM, 28031 Madrid, SpainIMDEA Networks Institute, 28918 Madrid, SpainIMDEA Networks Institute, 28918 Madrid, SpainGraph automorphism (GA) is a classical problem, in which the objective is to compute the automorphism group of an input graph. Most GA algorithms explore a search tree using the individualization-refinement procedure. Four novel techniques are proposed which increase the performance of any algorithm of this type by reducing 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 an input graph. Then, we describe how these 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. Using a benchmark of different graph families, we have evaluated the impact of these techniques on the size of the search tree, observing a significant reduction both when they are applied individually and when all of them are applied together. This is also reflected in a reduction of the running time, which is substantial for some graph families. Finally, we have compared the search tree size of conauto-2.03 against those of other popular GA algorithms, observing that, in most cases, conauto explores less nodes than these algorithms.http://dx.doi.org/10.1155/2014/934637 |
| spellingShingle | José Luis López-Presa Luis F. Chiroque Antonio Fernández Anta Novel Techniques to Speed Up the Computation of the Automorphism Group of a Graph Journal of Applied Mathematics |
| title | Novel Techniques to Speed Up the Computation of the Automorphism Group of a Graph |
| title_full | Novel Techniques to Speed Up the Computation of the Automorphism Group of a Graph |
| title_fullStr | Novel Techniques to Speed Up the Computation of the Automorphism Group of a Graph |
| title_full_unstemmed | Novel Techniques to Speed Up the Computation of the Automorphism Group of a Graph |
| title_short | Novel Techniques to Speed Up the Computation of the Automorphism Group of a Graph |
| title_sort | novel techniques to speed up the computation of the automorphism group of a graph |
| url | http://dx.doi.org/10.1155/2014/934637 |
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