Mixing time and long paths in graphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation Algorithms for the Unsplittable Flow Problem
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Random Structures & Algorithms
An algorithmic Friedman--Pippenger theorem on tree embeddings and applications to routing
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A logarithmic approximation for unsplittable flow on line graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Disjoint paths in sparse graphs
Discrete Applied Mathematics
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Approximation algorithms for edge-disjoint paths and unsplittable flow
Efficient Approximation and Online Algorithms
Routing in undirected graphs with constant congestion
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Random Structures & Algorithms
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Given a graph G=(V,E)and a set of $\kappa$ 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 $\kappa$ paths so found is edge-disjoint. For arbitrary graphs the problem is ${\cal NP}$-complete, although it is in ${\cal P}$ if $\kappa$ is fixed. We present a polynomial time randomized algorithm for finding edge-disjoint paths in an r-regular expander graph G. We show that if G has sufficiently strong expansion properties and r is sufficiently large, then all sets of $\kappa=\Omega(n/\log n)$ pairs of vertices can be joined. This is within a constant factor of best possible.