research-article

Symmetry Exploitation for Online Machine Covering with Bounded Migration

Authors:

José VerschaeAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 16, Issue 4

Article No.: 43, Pages 1 - 22

https://doi.org/10.1145/3397535

Published: 06 July 2020 Publication History

Abstract

Online models that allow recourse can be highly effective in situations where classical online models are too pessimistic. One such problem is the online machine covering problem on identical machines. In this setting, jobs arrive one by one and must be assigned to machines with the objective of maximizing the minimum machine load. When a job arrives, we are allowed to reassign some jobs as long as their total size is (at most) proportional to the processing time of the arriving job. The proportionality constant is called the migration factor of the algorithm.

Using a rounding procedure with useful structural properties for online packing and covering problems, we design first a simple (1.7 + ε)-competitive algorithm using a migration factor of O(1/ε), which maintains at every arrival a locally optimal solution with respect to the Jump neighborhood. After that, we present as our main contribution a more involved (4/3+ε)-competitive algorithm using a migration factor of Ō(1/ε ³). At every arrival, we run an adaptation of the Largest Processing Time first (LPT) algorithm. Since the new job can cause a complete change of the assignment of smaller jobs in both cases, a low migration factor is achieved by carefully exploiting the highly symmetric structure obtained by the rounding procedure.

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Cited By

Maack M(2023)Online load balancing on uniform machines with limited migrationOperations Research Letters10.1016/j.orl.2023.02.01351:3(220-225)Online publication date: 1-May-2023
https://dl.acm.org/doi/10.1016/j.orl.2023.02.013
Levin A(2023)Online Minimization of the Maximum Starting Time: Migration HelpsAlgorithmica10.1007/s00453-023-01097-085:8(2238-2259)Online publication date: 1-Aug-2023
https://dl.acm.org/doi/10.1007/s00453-023-01097-0
Albers SGálvez WJanke M(2023)Machine Covering in the Random-Order ModelAlgorithmica10.1007/s00453-022-01011-085:6(1560-1585)Online publication date: 1-Jun-2023
https://dl.acm.org/doi/10.1007/s00453-022-01011-0
Show More Cited By

Index Terms

Symmetry Exploitation for Online Machine Covering with Bounded Migration
1. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis
      1. Scheduling algorithms
    2. Online algorithms

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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 16, Issue 4

October 2020

404 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/3407674

Editor:
Aravind Srinivasan
University of Maryland, USA

Issue’s Table of Contents

Copyright © 2020 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 06 July 2020

Online AM: 07 May 2020

Accepted: 01 April 2020

Revised: 01 April 2020

Received: 01 April 2019

Published in TALG Volume 16, Issue 4

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Comisión Nacional de Investigación Científica y Tecnológica
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

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Cited By

Maack M(2023)Online load balancing on uniform machines with limited migrationOperations Research Letters10.1016/j.orl.2023.02.01351:3(220-225)Online publication date: 1-May-2023
https://dl.acm.org/doi/10.1016/j.orl.2023.02.013
Levin A(2023)Online Minimization of the Maximum Starting Time: Migration HelpsAlgorithmica10.1007/s00453-023-01097-085:8(2238-2259)Online publication date: 1-Aug-2023
https://dl.acm.org/doi/10.1007/s00453-023-01097-0
Albers SGálvez WJanke M(2023)Machine Covering in the Random-Order ModelAlgorithmica10.1007/s00453-022-01011-085:6(1560-1585)Online publication date: 1-Jun-2023
https://dl.acm.org/doi/10.1007/s00453-022-01011-0
Akaria IEpstein L(2023)Bin stretching with migration on two hierarchical machinesMathematical Methods of Operations Research10.1007/s00186-023-00830-398:1(111-153)Online publication date: 19-Jul-2023
https://doi.org/10.1007/s00186-023-00830-3
Akaria IEpstein L(2022)Online scheduling with migration on two hierarchical machinesJournal of Combinatorial Optimization10.1007/s10878-022-00906-644:5(3535-3548)Online publication date: 1-Dec-2022
https://dl.acm.org/doi/10.1007/s10878-022-00906-6
Kawase YSumita H(2022)Online Max-min Fair AllocationAlgorithmic Game Theory10.1007/978-3-031-15714-1_30(526-543)Online publication date: 12-Sep-2022
https://dl.acm.org/doi/10.1007/978-3-031-15714-1_30

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