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STOC
1992
ACM

Existence and Construction of Edge Disjoint Paths on Expander Graphs

13 years 9 months ago
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.
Andrei Z. Broder, Alan M. Frieze, Eli Upfal
Added 11 Aug 2010
Updated 11 Aug 2010
Type Conference
Year 1992
Where STOC
Authors Andrei Z. Broder, Alan M. Frieze, Eli Upfal
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