Existence and Construction of Edge Disjoint Paths on Expander Graphs

Given an expander graph G = (V, E) and a set of q disjoint pairs of vertices in V , we are interested in finding for each pair (ai, bi), a path connecting ai to bi, such that the set of q paths so found is edge-disjoint. (For general graphs the related decision problem is NPcomplete.) We prove sufficient conditions for the existence of edge-disjoint paths connecting any set of q n/(log n) disjoint pairs of vertices on any n vertex bounded degree expander, where depends only on the expansion properties of the input graph, and not on n. Furthermore, we present a randomized o(n3) time algorithm, and a random NC algorithm for constructing these paths. (Previous existence proofs and construction algorithms allowed only up to n pairs, for some 1/3, and strong expanders [19].) In passing, we develop an algorithm for splitting a sufficiently strong expander into two edge-disjoint spanning expanders.

• Type: Conference
• Year: 1992
• Where: STOC
• Authors: Andrei Z. Broder, Alan M. Frieze, Eli Upfal
• Keywords: Algorithms, Disjoint Pairs, Expander Graph, Path Connecting Ai, STOC 1992