article

Graph minimum linear arrangement by multilevel weighted edge contractions

Authors:

Achi BrandtAuthors Info & Claims

Journal of Algorithms, Volume 60, Issue 1

Pages 24 - 41

https://doi.org/10.1016/j.jalgor.2004.10.004

Published: 01 July 2006 Publication History

Abstract

The minimum linear arrangement problem is widely used and studied in many practical and theoretical applications. In this paper we present a linear-time algorithm for the problem inspired by the algebraic multigrid approach which is based on weighted edge contraction rather than simple contraction. Our results turned out to be better than every known result in almost all cases, while the short running time of the algorithm enabled experiments with very large graphs.

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Cited By

Liu XUshijima-Mwesigwa HGhosh ISafro I(2022)Partitioning Dense Graphs with Hardware AcceleratorsComputational Science – ICCS 202210.1007/978-3-031-08757-8_40(476-483)Online publication date: 21-Jun-2022
https://dl.acm.org/doi/10.1007/978-3-031-08757-8_40
Qiu ZShaydulin RLiu XAlexeev YHenry CSafro I(2021)ELRUNAACM Journal of Experimental Algorithmics10.1145/345070326(1-32)Online publication date: 9-Jul-2021
https://dl.acm.org/doi/10.1145/3450703
Ushijima-Mwesigwa HShaydulin RNegre CMniszewski SAlexeev YSafro I(2021)Multilevel Combinatorial Optimization across Quantum ArchitecturesACM Transactions on Quantum Computing10.1145/34256072:1(1-29)Online publication date: 13-Feb-2021
https://dl.acm.org/doi/10.1145/3425607
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Index Terms

Graph minimum linear arrangement by multilevel weighted edge contractions
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
      1. Combinatorial algorithms
    2. Graph theory
      1. Graph algorithms
  2. Mathematical analysis
    1. Differential equations
      1. Partial differential equations
    2. Mathematical optimization
2. Theory of computation
  1. Design and analysis of algorithms
    1. Mathematical optimization
  2. Randomness, geometry and discrete structures

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Published In

cover image Journal of Algorithms

Journal of Algorithms Volume 60, Issue 1

July 2006

83 pages

ISSN:0196-6774

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Publisher

Academic Press, Inc.

United States

Publication History

Published: 01 July 2006

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Cited By

Liu XUshijima-Mwesigwa HGhosh ISafro I(2022)Partitioning Dense Graphs with Hardware AcceleratorsComputational Science – ICCS 202210.1007/978-3-031-08757-8_40(476-483)Online publication date: 21-Jun-2022
https://dl.acm.org/doi/10.1007/978-3-031-08757-8_40
Qiu ZShaydulin RLiu XAlexeev YHenry CSafro I(2021)ELRUNAACM Journal of Experimental Algorithmics10.1145/345070326(1-32)Online publication date: 9-Jul-2021
https://dl.acm.org/doi/10.1145/3450703
Ushijima-Mwesigwa HShaydulin RNegre CMniszewski SAlexeev YSafro I(2021)Multilevel Combinatorial Optimization across Quantum ArchitecturesACM Transactions on Quantum Computing10.1145/34256072:1(1-29)Online publication date: 13-Feb-2021
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Valejo AFerreira VFabbri ROliveira MLopes A(2020)A Critical Survey of the Multilevel Method in Complex NetworksACM Computing Surveys10.1145/337934753:2(1-35)Online publication date: 17-Apr-2020
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Pardo EGarcía-Sánchez ASevaux MDuarte A(2020)Basic variable neighborhood search for the minimum sitting arrangement problemJournal of Heuristics10.1007/s10732-019-09432-x26:2(249-268)Online publication date: 1-Apr-2020
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Hager WHungerford JSafro I(2018)A multilevel bilinear programming algorithm for the vertex separator problemComputational Optimization and Applications10.1007/s10589-017-9945-269:1(189-223)Online publication date: 1-Jan-2018
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Glover FRego C(2017)New relationships for multi-neighborhood search for the minimum linear arrangement problemJournal of Discrete Algorithms10.1016/j.jda.2017.10.00346:C(16-24)Online publication date: 1-Sep-2017
https://dl.acm.org/doi/10.1016/j.jda.2017.10.003
Safro ISanders PSchulz C(2015)Advanced Coarsening Schemes for Graph PartitioningACM Journal of Experimental Algorithmics10.1145/267033819(1-24)Online publication date: 7-Jan-2015
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