License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2019.27
URN: urn:nbn:de:0030-drops-111488
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11148/
Chakrabarty, Deeparnab ;
Swamy, Chaitanya
Simpler and Better Algorithms for Minimum-Norm Load Balancing
Abstract
Recently, Chakrabarty and Swamy (STOC 2019) introduced the minimum-norm load-balancing problem on unrelated machines, wherein we are given a set J of jobs that need to be scheduled on a set of m unrelated machines, and a monotone, symmetric norm; We seek an assignment sigma: J -> [m] that minimizes the norm of the resulting load vector load_{sigma} in R_+^m, where load_{sigma}(i) is the load on machine i under the assignment sigma. Besides capturing all l_p norms, symmetric norms also capture other norms of interest including top-l norms, and ordered norms. Chakrabarty and Swamy (STOC 2019) give a (38+epsilon)-approximation algorithm for this problem via a general framework they develop for minimum-norm optimization that proceeds by first carefully reducing this problem (in a series of steps) to a problem called min-max ordered load balancing, and then devising a so-called deterministic oblivious LP-rounding algorithm for ordered load balancing.
We give a direct, and simple 4+epsilon-approximation algorithm for the minimum-norm load balancing based on rounding a (near-optimal) solution to a novel convex-programming relaxation for the problem. Whereas the natural convex program encoding minimum-norm load balancing problem has a large non-constant integrality gap, we show that this issue can be remedied by including a key constraint that bounds the "norm of the job-cost vector." Our techniques also yield a (essentially) 4-approximation for: (a) multi-norm load balancing, wherein we are given multiple monotone symmetric norms, and we seek an assignment respecting a given budget for each norm; (b) the best simultaneous approximation factor achievable for all symmetric norms for a given instance.
BibTeX - Entry
@InProceedings{chakrabarty_et_al:LIPIcs:2019:11148,
author = {Deeparnab Chakrabarty and Chaitanya Swamy},
title = {{Simpler and Better Algorithms for Minimum-Norm Load Balancing}},
booktitle = {27th Annual European Symposium on Algorithms (ESA 2019)},
pages = {27:1--27:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-124-5},
ISSN = {1868-8969},
year = {2019},
volume = {144},
editor = {Michael A. Bender and Ola Svensson and Grzegorz Herman},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/11148},
URN = {urn:nbn:de:0030-drops-111488},
doi = {10.4230/LIPIcs.ESA.2019.27},
annote = {Keywords: Approximation Algorithms}
}
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Keywords: |
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Approximation Algorithms |
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Collection: |
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27th Annual European Symposium on Algorithms (ESA 2019) |
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Issue Date: |
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2019 |
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Date of publication: |
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06.09.2019 |
