A Stochastic Heuristic for Visualising Graph Clusters in a Bi-DimensionalSpace Prior to Partitioning

  • Authors:
  • Pascale Kuntz;Dominique Snyers;Paul Layzell

  • Affiliations:
  • IRESTE, La Chantrerie, BP 60601, 44306 Nantes Cedex 3, France. pkuntz@ireste.fr;ENST de Bretagne, BP 832, Brest Cedex, France. Dominique.Snyers@enst-bretagne.fr;CCNR, COGS, University of Sussex, Brighton, England. paulla@cogs.susx.ac.uk

  • Venue:
  • Journal of Heuristics
  • Year:
  • 1999

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Abstract

This paper presents a new stochastic heuristic to reveal some structures inherent in large graphs, by displaying spatially separate clusters of highly connected vertex subsets on a two-dimensional grid. The algorithm employed is inspired by a biological model of ant behavior; it proceeds by local optimisations, and requires neither global criteria, nor any a priori knowledge of the graph. It is presented here as a preliminary phase in a recent approach to graph partitioning problems: transforming the combinatorial problem(minimising edge cuts) into one of clustering by constructing some bijectivemapping between the graph vertices and points in some geometric space. Afterreviewing different embeddings proposed in the literature, we define adissimilarity coefficient on the vertex set which translates the graph‘sinteresting structural properties into distances on the grid, and incorporateit into the clustering heuristic. The heuristic‘s performance on a well-knownclass of pseudo-random graphs is assessed according to several metric andcombinatorial criteria.