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Optimal Construction of Edge-Disjoint Paths in Random Regular Graphs

Published online by Cambridge University Press:  01 May 2000

ALAN M. FRIEZE
Affiliation:
Department of Mathematical Sciences, Carnegie-Mellon University, Pittsburgh, PA 15213, USA (e-mail: alan@random.math.cmu.edu, lzhao@andrew.cmu.edu)
LEI ZHAO
Affiliation:
Department of Mathematical Sciences, Carnegie-Mellon University, Pittsburgh, PA 15213, USA (e-mail: alan@random.math.cmu.edu, lzhao@andrew.cmu.edu)

Abstract

Given a graph G = (V, E) and a set of κ 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 κ paths so found is edge-disjoint. (For arbitrary graphs the problem is [Nscr ][Pscr ]-complete, although it is in [Pscr ] if κ is fixed.)

We present a polynomial time randomized algorithm for finding edge-disjoint paths in the random regular graph Gn,r, for sufficiently large r. (The graph is chosen first, then an adversary chooses the pairs of end-points.) We show that almost every Gn,r is such that all sets of κ = Ω(n/log n) pairs of vertices can be joined. This is within a constant factor of the optimum.

Type
Research Article
Copyright
2000 Cambridge University Press

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