Novel Techniques to Speed Up the Computation of the Automorphism Group of a Graph
Joint Authors
López-Presa, José Luis
Fernández Anta, Antonio
Chiroque, Luis F.
Source
Journal of Applied Mathematics
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-07-24
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
López-Presa, José Luis& Chiroque, Luis F.& Fernández Anta, Antonio. 2014. Novel Techniques to Speed Up the Computation of the Automorphism Group of a Graph. Journal of Applied Mathematics،Vol. 2014, no. 2014, pp.1-15.
https://search.emarefa.net/detail/BIM-509394
Modern Language Association (MLA)
López-Presa, José Luis…[et al.]. Novel Techniques to Speed Up the Computation of the Automorphism Group of a Graph. Journal of Applied Mathematics No. 2014 (2014), pp.1-15.
https://search.emarefa.net/detail/BIM-509394
American Medical Association (AMA)
López-Presa, José Luis& Chiroque, Luis F.& Fernández Anta, Antonio. Novel Techniques to Speed Up the Computation of the Automorphism Group of a Graph. Journal of Applied Mathematics. 2014. Vol. 2014, no. 2014, pp.1-15.
https://search.emarefa.net/detail/BIM-509394
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-509394