Approximation Algorithms for the Unsplittable Flow Problem
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Approximation algorithms for edge-disjoint paths and unsplittable flow
Efficient Approximation and Online Algorithms
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Given a digraph D = (V;A) and a set of k 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 k paths so found is arc-disjoint. For arbitrary graphs the problem is NP-complete, even for k = 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 propertiesand r is sufficiently large then all sets of k = \Omega (n/\log n) pairs of vertices can be joined. This is within a constant factor of best possible.