On the minimum path problem in Knödel graphs

Abstract

AbstractThe 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