Short length menger's theorem and reliable optical routing

In the minimum path coloring problem, we are given a graph and a set of pairs of vertices of the graph and we are asked to connect the pairs by colored paths in such a way that paths of the same color are edge disjoint. In this paper we deal with a generalization of this problem where we are asked to connect each pair by a k edge disjoint paths of the same color. The objective is to minimize the number of colors. The reason for multiple paths between the same pair of vertices is to ensure fault tolerance of the connections. We propose an O(k2 F) = O(k2 ∆α−1 log n) approximation algorithm for this problem where F is the flow number of the graph, ∆ is the maximum degree and α is the expansion. This is an improvement even for the special case k = 1 where, to our knowledge, the best bound known previously is weaker by a factor of log n. The underlying problem is that of finding several disjoint path between a given pair of vertices. Menger’s theorem provides necessary and su�...

• Type: Conference
• Year: 2003
• Where: SPAA
• Authors: Amitabha Bagchi, Amitabh Chaudhary, Petr Kolman
• Keywords: Disjoint Paths, Distributed And Parallel Computing, Edge Disjoint, Edge Disjoint Paths, SPAA 2003