Canonical Labelling of Site Graphs

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)

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.

In Ion Petre: Proceedings Fourth International Workshop on Computational Models for Cell Processes (CompMod 2013), Turku, Finland, 11th June 2013, Electronic Proceedings in Theoretical Computer Science 116, pp. 13–28.
Published: 9th June 2013.

ArXived at: http://dx.doi.org/10.4204/EPTCS.116.3 bibtex PDF
References in reconstructed bibtex, XML and HTML format (approximated).
Comments and questions to: eptcs@eptcs.org
For website issues: webmaster@eptcs.org