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Polynomial-Time Approximation Schemes for a Class of Integrated Network Design and Scheduling Problems with Parallel Identical Machines

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Combinatorial Optimization (ISCO 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13526))

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Abstract

In the integrated network design and scheduling problem (INDS-P), we are asked to repair edges in a graph by using parallel machines so that the performance of the network is recovered by a certain level, and the objective is to minimize the makespan required to finish repairing edges. The main aim of this paper is to show that polynomial-time approximation schemes exist for some class of the problem (INDS-P), including the problems associated with minimum spanning tree, shortest path, maximum flow with unit capacity, and maximum-weight matching.

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Notes

  1. 1.

    This problem is denoted as “\(Pm | \beta | C_\textrm{max}\)-Threshold” in [15].

  2. 2.

    By guessing we mean trying all possible assignments by enumeration.

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Authors and Affiliations

  1. Tokyo Institute of Technology, Tokyo, 152-8550, Japan

    Yusuke Saito & Akiyoshi Shioura

Authors
  1. Yusuke Saito
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  2. Akiyoshi Shioura
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Correspondence to Akiyoshi Shioura .

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Editors and Affiliations

  1. ESSEC Business School of Paris, Cergy Pontoise Cedex, France

    Ivana Ljubić

  2. IBM TJ Watson Research Center, Yorktown Heights, NY, USA

    Francisco Barahona

  3. Georgia Institute of Technology, Atlanta, GA, USA

    Santanu S. Dey

  4. Université Paris-Dauphine, Paris, France

    A. Ridha Mahjoub

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Saito, Y., Shioura, A. (2022). Polynomial-Time Approximation Schemes for a Class of Integrated Network Design and Scheduling Problems with Parallel Identical Machines. In: Ljubić, I., Barahona, F., Dey, S.S., Mahjoub, A.R. (eds) Combinatorial Optimization. ISCO 2022. Lecture Notes in Computer Science, vol 13526. Springer, Cham. https://doi.org/10.1007/978-3-031-18530-4_24

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  • DOI: https://doi.org/10.1007/978-3-031-18530-4_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-18529-8

  • Online ISBN: 978-3-031-18530-4

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