On the minimum path problem in Knödel graphs

  • Authors:

  • Hovhannes A. Harutyunyan;Calin D. Morosan

  • Affiliations:

  • Department of Computer Science, Concordia University, Montreal, Quebec, H3G 1M8, Canada;Department of Computer Science, Concordia University, Montreal, Quebec, H3G 1M8, Canada

  • Venue:
  • Networks
  • Year:
  • 2007

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Abstract

The Knödel graphs Wd,n are regular graphs, of even order n and degree d ≤ ⌊log n⌋. They have been introduced by W. Knödel as gossip graphs for d = ⌊log n⌋. A logarithmic algorithm for the minimum path problem in Knödel graphs is an open problem despite the fact that they are bipartite and highly symmetric. In this paper, we describe a logarithmic time two-approximation algorithm for the shortest path in the Knödel graph on 2d vertices with degree d. We also prove that for a subset of the set of vertices, the algorithm gives a minimum length path. © 2007 Wiley Periodicals, Inc. NETWORKS, Vol. 50(1), 86–91 2007