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Online makespan scheduling with job migration on uniform machines
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Englert, Matthias, Mezlaf, David and Westermann, Matthias (2018) Online makespan scheduling with job migration on uniform machines. In: 26th Annual European Symposium on Algorithms (ESA 2018), Helsinki, Finland, 20-24 Aug 2018. Published in: 26th Annual European Symposium on Algorithms (ESA 2018), 112 pp. 1-14. ISBN 9783959770811. doi:10.4230/LIPIcs.ESA.2018.26 ISSN 1868-8969.
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Official URL: https://doi.org/10.4230/LIPIcs.ESA.2018.26
Abstract
In the classic minimum makespan scheduling problem, we are given an input sequence of n jobs with sizes. A scheduling algorithm has to assign the jobs to m parallel machines. The objective is to minimize the makespan, which is the time it takes until all jobs are processed. In this paper, we consider online scheduling algorithms without preemption. However, we allow the online algorithm to reassign up to k jobs to different machines in the final assignment. For m identical machines, Albers and Hellwig (Algorithmica, 2017) give tight bounds on the competitive ratio in this model. The precise ratio depends on, and increases with, m. It lies between 4/3 and ~~ 1.4659. They show that k = O(m) is sufficient to achieve this bound and no k = o(n) can result in a better bound. We study m uniform machines, i.e., machines with different speeds, and show that this setting is strictly harder. For sufficiently large m, there is a delta = Theta(1) such that, for m machines with only two different machine speeds, no online algorithm can achieve a competitive ratio of less than 1.4659 + delta with k = o(n). We present a new algorithm for the uniform machine setting. Depending on the speeds of the machines, our scheduling algorithm achieves a competitive ratio that lies between 4/3 and ~~ 1.7992 with k = O(m). We also show that k = Omega(m) is necessary to achieve a competitive ratio below 2. Our algorithm is based on a subtle imbalance with respect to the completion times of the machines, complemented by a bicriteria approximation algorithm that minimizes the makespan and maximizes the average completion time for certain sets of machines.
| Item Type: | Conference Item (Paper) | ||||||
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| Subjects: | Q Science > QA Mathematics > QA75 (Please use QA76 Electronic Computers. Computer Science) | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||||
| Library of Congress Subject Headings (LCSH): | Computer scheduling, Online algorithms, Parallel processing (Electronic computers) | ||||||
| Series Name: | Leibniz International Proceedings in Informatics (LIPIcs) | ||||||
| Journal or Publication Title: | 26th Annual European Symposium on Algorithms (ESA 2018) | ||||||
| Publisher: | Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik | ||||||
| Place of Publication: | Dagstuhl, Germany | ||||||
| ISBN: | 9783959770811 | ||||||
| ISSN: | 1868-8969 | ||||||
| Editor: | Azar , Yossi and Bast , Hannah and Herman, Grzegorz | ||||||
| Official Date: | 8 August 2018 | ||||||
| Dates: |
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| Volume: | 112 | ||||||
| Page Range: | pp. 1-14 | ||||||
| Article Number: | 26 | ||||||
| DOI: | 10.4230/LIPIcs.ESA.2018.26 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||
| Date of first compliant deposit: | 20 August 2018 | ||||||
| Date of first compliant Open Access: | 20 August 2018 | ||||||
| Conference Paper Type: | Paper | ||||||
| Title of Event: | 26th Annual European Symposium on Algorithms (ESA 2018) | ||||||
| Type of Event: | Conference | ||||||
| Location of Event: | Helsinki, Finland | ||||||
| Date(s) of Event: | 20-24 Aug 2018 | ||||||
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