research-article

Sum edge coloring of multigraphs via configuration LP

Authors:

Magnús M. Halldórsson,

Guy Kortsarz, and

Maxim SviridenkoAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 7, Issue 2

Article No.: 22, Pages 1 - 21

https://doi.org/10.1145/1921659.1921668

Published: 31 March 2011 Publication History

Abstract

We consider the scheduling of biprocessor jobs under sum objective (BPSMSM). Given a collection of unit-length jobs where each job requires the use of two processors, find a schedule such that no two jobs involving the same processor run concurrently. The objective is to minimize the sum of the completion times of the jobs. Equivalently, we would like to find a sum edge coloring of a given multigraph, that is, a partition of its edge set into matchings M₁,…,M_t minimizing Σ_i=1^ti|M_i|.

This problem is APX-hard, even in the case of bipartite graphs [Marx 2009]. This special case is closely related to the classic open shop scheduling problem. We give a 1.8298-approximation algorithm for BPSMSM improving the previously best ratio known of 2 [Bar-Noy et al. 1998]. The algorithm combines a configuration LP with greedy methods, using nonstandard randomized rounding on the LP fractions. We also give an efficient combinatorial 1.8886-approximation algorithm for the case of simple graphs, which gives an improved 1.79568 + O(log d¯/d¯)-approximation in graphs of large average degree d¯.

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Cited By

DeHaan IFriggstad Z(2023)Approximate Minimum Sum Colorings and Maximum k-Colorable Subgraphs of Chordal GraphsAlgorithms and Data Structures10.1007/978-3-031-38906-1_22(326-339)Online publication date: 31-Jul-2023
https://dl.acm.org/doi/10.1007/978-3-031-38906-1_22
Epstein LLevin A(2019)On the performance guarantee of First Fit for sum coloringJournal of Computer and System Sciences10.1016/j.jcss.2018.08.00299(91-105)Online publication date: Feb-2019
https://doi.org/10.1016/j.jcss.2018.08.002
Friggstad ZGolestanian AKhodamoradi KMartin CRahgoshay MRezapour MSalavatipour MZhang Y(2019)Scheduling problems over a network of machinesJournal of Scheduling10.1007/s10951-018-0591-z22:2(239-253)Online publication date: 1-Apr-2019
https://dl.acm.org/doi/10.1007/s10951-018-0591-z

Index Terms

Sum edge coloring of multigraphs via configuration LP
1. Mathematics of computing
  1. Mathematical analysis
    1. Mathematical optimization
      1. Continuous optimization
        Linear programming
2. Theory of computation
  1. Design and analysis of algorithms
  2. Theory and algorithms for application domains
    1. Machine learning theory
      1. Reinforcement learning
        Sequential decision making

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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 7, Issue 2

March 2011

284 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/1921659

Issue’s Table of Contents

Copyright © 2011 ACM.

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Association for Computing Machinery

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Publication History

Published: 31 March 2011

Accepted: 01 September 2010

Revised: 01 August 2010

Received: 01 March 2008

Published in TALG Volume 7, Issue 2

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Cited By

DeHaan IFriggstad Z(2023)Approximate Minimum Sum Colorings and Maximum k-Colorable Subgraphs of Chordal GraphsAlgorithms and Data Structures10.1007/978-3-031-38906-1_22(326-339)Online publication date: 31-Jul-2023
https://dl.acm.org/doi/10.1007/978-3-031-38906-1_22
Epstein LLevin A(2019)On the performance guarantee of First Fit for sum coloringJournal of Computer and System Sciences10.1016/j.jcss.2018.08.00299(91-105)Online publication date: Feb-2019
https://doi.org/10.1016/j.jcss.2018.08.002
Friggstad ZGolestanian AKhodamoradi KMartin CRahgoshay MRezapour MSalavatipour MZhang Y(2019)Scheduling problems over a network of machinesJournal of Scheduling10.1007/s10951-018-0591-z22:2(239-253)Online publication date: 1-Apr-2019
https://dl.acm.org/doi/10.1007/s10951-018-0591-z

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