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Computer Science > Discrete Mathematics

arXiv:1306.2405v1 (cs)
[Submitted on 11 Jun 2013]

Title:Canonical Labelling of Site Graphs

Authors:Nicolas Oury (School of Informatics, Edinburgh University, Edinburgh, Scotland), Michael Pedersen (Department of Plant Sciences, Cambridge University, Cambridge, UK), Rasmus Petersen (Microsoft Research, Cambridge, UK)
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Abstract:We investigate algorithms for canonical labelling of site graphs, i.e. graphs in which edges bind vertices on sites with locally unique names. We first show that the problem of canonical labelling of site graphs reduces to the problem of canonical labelling of graphs with edge colourings. We then present two canonical labelling algorithms based on edge enumeration, and a third based on an extension of Hopcroft's partition refinement algorithm. All run in quadratic worst case time individually. However, one of the edge enumeration algorithms runs in sub-quadratic time for graphs with "many" automorphisms, and the partition refinement algorithm runs in sub-quadratic time for graphs with "few" bisimulation equivalences. This suite of algorithms was chosen based on the expectation that graphs fall in one of those two categories. If that is the case, a combined algorithm runs in sub-quadratic worst case time. Whether this expectation is reasonable remains an interesting open problem.
Comments: In Proceedings CompMod 2013, arXiv:1306.2019
Subjects: Discrete Mathematics (cs.DM); Combinatorics (math.CO)
Cite as: arXiv:1306.2405 [cs.DM]
  (or arXiv:1306.2405v1 [cs.DM] for this version)
  https://doi.org/10.48550/arXiv.1306.2405
Journal reference: EPTCS 116, 2013, pp. 13-28
Related DOI: https://doi.org/10.4204/EPTCS.116.3

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Tue, 11 Jun 2013 02:02:41 UTC (86 KB)
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