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Arc-disjoint paths in expander digraphs

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2 Author(s)
Bohman, T. ; Dept. of Math. Sci., Carnegie Mellon Univ., Pittsburgh, PA, USA ; Frieze, A.

Given a digraph D=(V, A) and a set of κ pairs of vertices in V, we are interested in finding for each pair (xi, yi), a directed path connecting xi to yi, such that the set of κ paths so found is arc-disjoint. For arbitrary graphs, the problem is 𝒩𝒫-complete, even for κ=2. We present a polynomial time randomized algorithm for finding arc-disjoint paths in an r-regular expander digraph D. We show that if D has sufficiently strong expansion properties and r is sufficiently large, then all sets of κ=Ω(n/log n) pairs of vertices can be joined. This is within a constant factor of best possible.

Published in:

Foundations of Computer Science, 2001. Proceedings. 42nd IEEE Symposium on

Date of Conference:

8-11 Oct. 2001