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.ICALP.2017.12
URN: urn:nbn:de:0030-drops-73839
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7383/
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Nagarajan, Viswanath ; Shen, Xiangkun

Online Covering with Sum of $ell_q$-Norm Objectives

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LIPIcs-ICALP-2017-12.pdf (0.9 MB)

Abstract

We consider fractional online covering problems with lq-norm objectives. The problem of interest is of the form min{ f(x) : Ax >= 1, x >= 0} where f(x) is the weighted sum of lq-norms and A is a non-negative matrix. The rows of A (i.e. covering constraints) arrive online over time. We provide an online O(log d+log p)-competitive algorithm where p is the maximum to minimum ratio of A and A is the row sparsity of A. This is based on the online primal-dual framework where we use the dual of the above convex program. Our result expands the class of convex objectives that admit good online algorithms: prior results required a monotonicity condition on the objective which is not satisfied here. This result is nearly tight even for the linear special case. As direct applications, we obtain (i) improved online algorithms for non-uniform buy-at-bulk network design and (ii) the first online algorithm for throughput maximization under lq-norm edge capacities.

BibTeX - Entry

@InProceedings{nagarajan_et_al:LIPIcs:2017:7383,
  author =	{Viswanath Nagarajan and Xiangkun Shen},
  title =	{{Online Covering with Sum of $ell_q$-Norm Objectives}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{12:1--12:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Ioannis Chatzigiannakis and Piotr Indyk and Fabian Kuhn and Anca Muscholl},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7383},
  URN =		{urn:nbn:de:0030-drops-73839},
  doi =		{10.4230/LIPIcs.ICALP.2017.12},
  annote =	{Keywords: online algorithm, covering/packing problem, convex, buy-at-bulk, throughput maximization}
}

Keywords: online algorithm, covering/packing problem, convex, buy-at-bulk, throughput maximization
Collection: 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)
Issue Date: 2017
Date of publication: 07.07.2017

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