Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
Random sampling in cut, flow, and network design problems
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Existence and Construction of Edge-Disjoint Pathson Expander Graphs
SIAM Journal on Computing
Approximations for the disjoint paths problem in high-diameter planar networks
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Improved bounds for all optical routing
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Random Sampling in Cut, Flow, and Network Design Problems
Mathematics of Operations Research
Simple on-line algorithms for the maximum disjoint paths problem
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Approximate Max-Flow Min-(Multi)Cut Theorems and Their Applications
SIAM Journal on Computing
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
ICALP '93 Proceedings of the 20th International Colloquium on Automata, Languages and Programming
Disjoint paths in densely embedded graphs
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Improved approximations for edge-disjoint paths, unsplittable flow, and related routing problems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Short paths in expander graphs
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Approximation algorithms for disjoint paths problems
Approximation algorithms for disjoint paths problems
Graph decomposition and a greedy algorithm for edge-disjoint paths
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
New hardness results for congestion minimization and machine scheduling
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
The all-or-nothing multicommodity flow problem
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Approximate max-integral-flow/min-multicut theorems
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Edge-Disjoint Paths in Planar Graphs
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Multicommodity flow, well-linked terminals, and routing problems
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Hardness of the undirected edge-disjoint paths problem
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Hardness of the undirected congestion minimization problem
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Hardness of the Undirected Edge-Disjoint Paths Problem with Congestion
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
An Approximation Algorithm for the Disjoint Paths Problem in Even-Degree Planar Graphs
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Graph partitioning using single commodity flows
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Logarithmic hardness of the directed congestion minimization problem
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Edge-disjoint paths in Planar graphs with constant congestion
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Hardness of routing with congestion in directed graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
On partitioning graphs via single commodity flows
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
On-line admission control and circuit routing for high performance computing and communication
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
| Hi-index | 0.00 |
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.