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Logarithmic hardness of the directed congestion minimization problem

Published: 21 May 2006 Publication History

Abstract

We show that for any constant ε > 0, there is no Ω(log1-εM)-approximation algorithm for the directed congestion minimization problem 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.

References

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M. Andrews and L. Zhang. Hardness of the undirected congestion minimization problem. In Proceedings of the 37th Annual ACM Symposium on Theory of Computing, Baltimore, MD, May 2005.
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J. Chuzhoy and J. Naor. New hardness results for congestion minimization and machine scheduling. In Proceedings of the 36th Annual ACM Symposium of Theory of Computing, pages 28 -- 34, Chicago, IL, 2004.
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V. Guruswami, S. Khanna, R. Rajaraman, B. Shepherd, and M. Yannakakis. Near-optimal hardness results and approximation algorithms for edge-disjoint paths and related problems. In Proceedings of the 31st Annual ACM Symposium of Theory of Computing, pages 19--28, Atlanta, GA, May 1999.
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P. Raghavan and C.D. Thompson. Randomized rounding: a technique for provably good algorithms and algorithmic proofs. Combinatorica, 7:365 -- 374, 1991.
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Cited By

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  • (2017)Hardness of Routing for Minimizing Superlinear Polynomial Cost in Directed GraphsTheory and Applications of Models of Computation10.1007/978-3-319-55911-7_41(571-585)Online publication date: 21-Mar-2017
  • (2010)Approximation Algorithms for the Edge-Disjoint Paths Problem via Raecke DecompositionsProceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science10.1109/FOCS.2010.33(277-286)Online publication date: 23-Oct-2010
  • (2010)Inapproximability of Edge-Disjoint Paths and low congestion routing on undirected graphsCombinatorica10.1007/s00493-010-2455-930:5(485-520)Online publication date: 1-Sep-2010
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    cover image ACM Conferences
    STOC '06: Proceedings of the thirty-eighth annual ACM symposium on Theory of Computing
    May 2006
    786 pages
    ISBN:1595931341
    DOI:10.1145/1132516
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    Publication History

    Published: 21 May 2006

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    Author Tags

    1. congestion minimization
    2. directed graphs
    3. hardness of approximation

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    STOC06: Symposium on Theory of Computing
    May 21 - 23, 2006
    WA, Seattle, USA

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    Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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    Cited By

    View all
    • (2017)Hardness of Routing for Minimizing Superlinear Polynomial Cost in Directed GraphsTheory and Applications of Models of Computation10.1007/978-3-319-55911-7_41(571-585)Online publication date: 21-Mar-2017
    • (2010)Approximation Algorithms for the Edge-Disjoint Paths Problem via Raecke DecompositionsProceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science10.1109/FOCS.2010.33(277-286)Online publication date: 23-Oct-2010
    • (2010)Inapproximability of Edge-Disjoint Paths and low congestion routing on undirected graphsCombinatorica10.1007/s00493-010-2455-930:5(485-520)Online publication date: 1-Sep-2010
    • (2009)Polynomial flow-cut gaps and hardness of directed cut problemsJournal of the ACM10.1145/1502793.150279556:2(1-28)Online publication date: 17-Apr-2009
    • (2007)Polynomial flow-cut gaps and hardness of directed cut problemsProceedings of the thirty-ninth annual ACM symposium on Theory of computing10.1145/1250790.1250817(179-188)Online publication date: 11-Jun-2007
    • (2007)Hardness of routing with congestion in directed graphsProceedings of the thirty-ninth annual ACM symposium on Theory of computing10.1145/1250790.1250816(165-178)Online publication date: 11-Jun-2007
    • (2006)Logarithmic hardness of the undirected edge-disjoint paths problemJournal of the ACM10.1145/1183907.118391053:5(745-761)Online publication date: 1-Sep-2006
    • (2006)New hardness results for congestion minimization and machine schedulingJournal of the ACM10.1145/1183907.118390853:5(707-721)Online publication date: 1-Sep-2006
    • (2006)The NP-completeness columnACM Transactions on Algorithms10.1145/1159892.11599012:3(473-489)Online publication date: 1-Jul-2006
    • (2006)Edge disjoint paths in moderately connected graphsProceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I10.1007/11786986_19(202-213)Online publication date: 10-Jul-2006

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