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Graph Partitioning with Self-Organizing Maps

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  • Eric Bonabeau
  • Florian Henaux

Abstract

Self-organizing maps with variable local topology are shown to constitute a reasonably good heuristic to find approximate solutions to the NP-complete k-way graph partitioning problem, where a weighted graph has to be divided into k clusters of equal size while minimizing the total weight of inter-cluster edges. The equal size constraint is implemented through a distribution of training points that the map tends to approximate, and the minimal cut constraint is implemented through the simultaneous update of neighboring nodes. A mean-field analysis suggests that the complexity of the algorithm is at most in , where n is the number of vertices of the graph, and the number of edges. This prediction is tested on a class of random graphs. Submitted to: Neurocomputing.

Suggested Citation

  • Eric Bonabeau & Florian Henaux, 1998. "Graph Partitioning with Self-Organizing Maps," Working Papers 98-07-062, Santa Fe Institute.
    • Handle: RePEc:wop:safiwp:98-07-062
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    Keywords

    Neural networks; self-organizing maps; graph partitioning;
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