Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
SIAM Journal on Computing
Multicommodity Flow and Circuit Switching
HICSS '98 Proceedings of the Thirty-First Annual Hawaii International Conference on System Sciences-Volume 7 - Volume 7
New hardness results for congestion minimization and machine scheduling
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Hardness of Buy-at-Bulk Network Design
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
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
Hardness of routing with congestion in directed graphs
Proceedings of the thirty-ninth 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
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Given a set of demands in a directed graph, the directed congestion minimization problem is to route every demand with the objective of minimizing the heaviest load over all edges. We show that for any constant ϵ 0, there is no Ω(log1−ϵ M)-approximation algorithm on networks of size M unless NP ⊆ ZPTIME(npolylog n). This bound is almost tight given the O(log M/log log M)-approximation via randomized rounding due to Raghavan and Thompson.