A genetic algorithm for finding the pagenumber of interconnection networks

Authors:
Nidhi Kapoor;Mark Russell;Ivan Stojmenovic;Albert Y. Zomaya
Affiliations:
Nortel Networks, Ottawa, Ontario, Canada;Department of Combinatorics and Optimization, University of Waterloo, Waterloo, N2L 3G1 Ontario, Canada;SITE, University of Ottawa, Ottawa, K1N 6N5 Ontario, Canada/ and DISCA, IIMAS, UNAM, Ciudad Universitaria, Coyoacan, Mexico D.F. 04510, Mexico;Department of Electrical and Electronic Engineering, University of Western Australia, Perth, Western Australia 6907, Australia
Venue:
Journal of Parallel and Distributed Computing
Year:
2002

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Abstract

A "book-embedding" of a graph G comprises embedding the graph's nodes along the spine of a book and embedding the edges on the pages so that the edges embedded on the same page do not intersect. This is also referred to as the page model. The "pagenumber" of a graph is the thickness of the smallest (in number of pages) book into which G can be embedded. The problem has been studied only for some specific kind of graphs. The pagenumber problem is known to be NP-complete, even if the order of nodes on the spine is fixed. Using genetic algorithms, we describe the first algorithm for solving the pagenumber problem that can be applied on arbitrary graphs. Experimental results for several kinds of graphs are obtained. We were particularly interested in graphs that correspond to some well-known interconnection networks (such as hypercubes and meshes). We also introduced and experimented with 2-D pagenumber model for embedding graphs.