Optimal construction of edge-disjoint paths in random regular graphs
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
New algorithmic aspects of the Local Lemma with applications to routing and partitioning
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A deterministic approximation algorithm for a minmax integer programming problem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Edge-disjoint paths in expander graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
I/O-efficient techniques for computing pagerank
Proceedings of the eleventh international conference on Information and knowledge management
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Disjoint Paths in Expander Graphs via Random Walks: A Short Survey
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
Optimal Construction of Edge-Disjoint Paths in Random Regular Graphs
Combinatorics, Probability and Computing
The all-or-nothing multicommodity flow problem
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Multicommodity flow, well-linked terminals, and routing problems
Proceedings of the thirty-seventh 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
Almost-tight hardness of directed congestion minimization
Journal of the ACM (JACM)
Operations Research Letters
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Given a set of request pairs in a network, the problem of routing virtual circuits with low congestion is to connect each pair by a path so that few paths use the same link in the network. We build on an earlier multicommodity flow based approach of Leighton and Rao to show that ``short'' flow-paths lead to path-selections with ``low'' congestion. This shows that such good path-selections exist for constant-degree expanders with ``strong'' expansion, generalizing a result of Broder, Frieze and Upfal. We also show, for infinitely many n, n-vertex undirected graphs along with a set T of connection requests, such that: (a) T is fractionally realizable using flow-paths that impose a (fractional) congestion of at most 1; but (b) any rounding of such a flow to the given set of flow-paths, leads to a congestion of Omega(log n /loglog n). This is progress on a long-standing open problem.