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Almost-tight hardness of directed congestion minimization

Authors:

Matthew Andrews,

Lisa ZhangAuthors Info & Claims

Journal of the ACM (JACM), Volume 55, Issue 6

Article No.: 27, Pages 1 - 20

https://doi.org/10.1145/1455248.1455251

Published: 17 December 2008 Publication History

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Abstract

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(log^1−ε M)-approximation algorithm on networks of size M unless NP ⊆ ZPTIME(n^{polylog n}). This bound is almost tight given the O(log M/log log M)-approximation via randomized rounding due to Raghavan and Thompson.

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Cited By

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Chuzhoy J(2016)Routing in Undirected Graphs with Constant CongestionSIAM Journal on Computing10.1137/13091046445:4(1490-1532)Online publication date: Jan-2016
https://doi.org/10.1137/130910464
Cao ZWu CBerry M(2016)On Routing of Multiple Concurrent User Requests in Multi-Radio Multi-Channel Wireless Mesh Networks2016 17th International Conference on Parallel and Distributed Computing, Applications and Technologies (PDCAT)10.1109/PDCAT.2016.021(24-29)Online publication date: Dec-2016
https://doi.org/10.1109/PDCAT.2016.021
Trevisan L(2014)Inapproximability of Combinatorial Optimization ProblemsParadigms of Combinatorial Optimization10.1002/9781119005353.ch13(381-434)Online publication date: 8-Aug-2014
https://doi.org/10.1002/9781119005353.ch13
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Index Terms

Almost-tight hardness of directed congestion minimization
1. Theory of computation
  1. Design and analysis of algorithms

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Hardness of the Undirected Congestion Minimization Problem

We show that there is no $\gamma\log\log M/\log\log\log M$-approximation for the undirected congestion minimization problem unless $NP \subseteq ZPTIME(n^{{\rm polylog} n})$, where $M$ is the size of the graph and γ is some positive constant.
Logarithmic hardness of the directed congestion minimization problem
STOC '06: Proceedings of the thirty-eighth annual ACM symposium on Theory of Computing

We show that for any constant ε > 0, there is no Ω(log^1-εM)-approximation algorithm for the directed congestion minimization problem on networks of size M unless NP ⊆ ZPTIME(n^{polylog n}). This bound is almost tight given the O(log M/ log log M)-...
Hardness of the undirected congestion minimization problem
STOC '05: Proceedings of the thirty-seventh annual ACM symposium on Theory of computing

We show that there is no (log log M)^1-ε approximation for the undirected congestion minimization problem unless NP ⊆ ZPTIME(n^polylogn), where M is the size of the graph and ε is any positive constant.

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Published In

Journal of the ACM Volume 55, Issue 6

December 2008

114 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/1455248

Issue’s Table of Contents

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Association for Computing Machinery

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Publication History

Published: 17 December 2008

Accepted: 01 September 2008

Revised: 01 September 2008

Received: 01 November 2006

Published in JACM Volume 55, Issue 6

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Chuzhoy J(2016)Routing in Undirected Graphs with Constant CongestionSIAM Journal on Computing10.1137/13091046445:4(1490-1532)Online publication date: Jan-2016
https://doi.org/10.1137/130910464
Cao ZWu CBerry M(2016)On Routing of Multiple Concurrent User Requests in Multi-Radio Multi-Channel Wireless Mesh Networks2016 17th International Conference on Parallel and Distributed Computing, Applications and Technologies (PDCAT)10.1109/PDCAT.2016.021(24-29)Online publication date: Dec-2016
https://doi.org/10.1109/PDCAT.2016.021
Trevisan L(2014)Inapproximability of Combinatorial Optimization ProblemsParadigms of Combinatorial Optimization10.1002/9781119005353.ch13(381-434)Online publication date: 8-Aug-2014
https://doi.org/10.1002/9781119005353.ch13
(2014)General BibliographyParadigms of Combinatorial Optimization10.1002/9781119005353.biblio(707-765)Online publication date: 8-Aug-2014
https://doi.org/10.1002/9781119005353.biblio
Trevisan L(2013)Inapproximability of Combinatorial Optimization ProblemsParadigms of Combinatorial Optimization10.1002/9781118600207.ch13(381-434)Online publication date: 13-Feb-2013
https://doi.org/10.1002/9781118600207.ch13
Chuzhoy JKarloff HPitassi T(2012)Routing in undirected graphs with constant congestionProceedings of the forty-fourth annual ACM symposium on Theory of computing10.1145/2213977.2214054(855-874)Online publication date: 19-May-2012
https://dl.acm.org/doi/10.1145/2213977.2214054

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Hardness of the Undirected Congestion Minimization Problem

Logarithmic hardness of the directed congestion minimization problem

Hardness of the undirected congestion minimization problem

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