Starting time minimization for the maximum job variant

Leah Epstein; Asaf Levin

doi:10.1016/j.dam.2021.10.013

Starting time minimization for the maximum job variant

Leah Epstein, Asaf Levin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider a scheduling problem on identical machines, where the cost for each machine is the total size of jobs assigned to it, excluding its largest job. The objective is to minimize the cost of the schedule, which is the maximum cost over all machines. We study online algorithms with and without migration. We design an algorithm with competitive ratio 3 for the purely online variant and provide a lower bound of 2.26953 on the competitive ratio of any online algorithm. For two machines, we find tight bounds of 2 on the competitive ratio. Additionally, we design a polynomial time approximation scheme for the variant with migration. We also briefly discuss the same online problem on uniformly related machines.

Original language	English
Pages (from-to)	79-87
Number of pages	9
Journal	Discrete Applied Mathematics
Volume	307
DOIs	https://doi.org/10.1016/j.dam.2021.10.013
State	Published - 30 Jan 2022

Bibliographical note

Publisher Copyright:
© 2021 Elsevier B.V.

Keywords

Competitive analysis
Load balancing
Multiprocessor
Scheduling

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2021.10.013

Cite this

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AB - We consider a scheduling problem on identical machines, where the cost for each machine is the total size of jobs assigned to it, excluding its largest job. The objective is to minimize the cost of the schedule, which is the maximum cost over all machines. We study online algorithms with and without migration. We design an algorithm with competitive ratio 3 for the purely online variant and provide a lower bound of 2.26953 on the competitive ratio of any online algorithm. For two machines, we find tight bounds of 2 on the competitive ratio. Additionally, we design a polynomial time approximation scheme for the variant with migration. We also briefly discuss the same online problem on uniformly related machines.

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Starting time minimization for the maximum job variant

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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