The disjoint paths problem: algorithm and structure
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
A general framework for graph sparsification
Proceedings of the forty-third annual ACM symposium on Theory of computing
Breaking o(n1/2)-approximation algorithms for the edge-disjoint paths problem with congestion two
Proceedings of the forty-third annual ACM symposium on Theory of computing
On vertex sparsifiers with Steiner nodes
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Approximation algorithms and hardness of integral concurrent flow
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Routing in undirected graphs with constant congestion
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Large-treewidth graph decompositions and applications
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We study the edge disjoint paths (EDP) problem in undirected graphs: Given a graph $G$ with $n$ nodes and a set $\mathcal{T}$ of pairs of terminals, connect as many terminal pairs as possible using paths that are mutually edge disjoint. This leads to a variety of classic NP-complete problems, for which approximability is not well understood. We show a polylogarithmic approximation algorithm for the undirected EDP problem in general graphs with a moderate restriction on graph connectivity; we require the global minimum cut of $G$ to be $\Omega(\log^5n)$. Previously, constant or polylogarithmic approximation algorithms were known for trees with parallel edges, expanders, grids, grid-like graphs, and, most recently, even-degree planar graphs. These graphs either have special structure (e.g., they exclude minors) or have large numbers of short disjoint paths. Our algorithm extends previous techniques in that it applies to graphs with high diameters and asymptotically large minors.