Weighted Completion Time Minimization for Capacitated Parallel Machines

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We consider the weighted completion time minimization problem for capacitated parallel machines, which is a fundamental problem in modern cloud computing environments. We study settings in which the processed jobs may have varying duration, resource requirements and importance (weight). Each server (machine) can process multiple concurrent jobs up to its capacity. Due to the problem’s NP -hardness, we study heuristic approaches with provable approximation guarantees. We first analyze an algorithm that prioritizes the jobs with the smallest volume-by-weight ratio. We bound its approximation ratio with a decreasing function of the ratio between the highest resource demand of any job to the server’s capacity. Then, we use the algorithm for scheduling jobs with resource demands equal to or smaller than 0.5 of the server’s capacity in conjunction with the classic weighted shortest processing time algorithm for jobs with resource demands higher than 0.5. We thus create a hybrid, constant approximation algorithm for two or more machines. We also develop a constant approximation algorithm for the case with a single machine. This research is the first, to the best of our knowledge, to propose a polynomial-time algorithm with a constant approximation ratio for minimizing the weighted sum of job completion times for capacitated parallel machines.

Original languageEnglish
Title of host publicationApproximation and Online Algorithms - 19th International Workshop, WAOA 2021, Revised Selected Papers
EditorsJochen Koenemann, Britta Peis
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages14
ISBN (Print)9783030927011
StatePublished - 2021
Event19th International Workshop on Approximation and Online Algorithms, WAOA 2021 - Virtual, Online
Duration: 6 Sep 202110 Sep 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12982 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference19th International Workshop on Approximation and Online Algorithms, WAOA 2021
CityVirtual, Online

Bibliographical note

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.


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