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DOI: 10.4230/LIPIcs.ICALP.2016.54
URN: urn:nbn:de:0030-drops-63344
URL: http://drops.dagstuhl.de/opus/volltexte/2016/6334/
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Marasevic, Jelena ; Stein, Clifford ; Zussman, Gil

A Fast Distributed Stateless Algorithm for alpha-Fair Packing Problems

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LIPIcs-ICALP-2016-54.pdf (0.6 MB)


Abstract

We study weighted alpha-fair packing problems, that is, the problems of maximizing the objective functions (i) sum_j w_j*x_j^{1-alpha}/(1-alpha) when alpha > 0, alpha != 1 and (ii) sum_j w_j*ln(x_j) when alpha = 1, over linear constraints A*x <=b, x >= 0, where wj are positive weights and A and b are non-negative. We consider the distributed computation model that was used for packing linear programs and network utility maximization problems. Under this model, we provide a distributed algorithm for general alpha that converges to an epsilon-approximate solution in time (number of distributed iterations) that has an inverse polynomial dependence on the approximation parameter epsilon and poly-logarithmic dependence on the problem size. This is the first distributed algorithm for weighted alpha-fair packing with poly-logarithmic convergence in the input size. The algorithm uses simple local update rules and is stateless (namely, it allows asynchronous updates, is self-stabilizing, and allows incremental and local adjustments). We also obtain a number of structural results that characterize alpha-fair allocations as the value of alpha is varied. These results deepen our understanding of fairness guarantees in alpha-fair packing allocations, and also provide insight into the behavior of alpha-fair allocations in the asymptotic cases alpha -> 0, alpha -> 1, and alpha -> infinity.

BibTeX - Entry

@InProceedings{marasevic_et_al:LIPIcs:2016:6334,
  author =	{Jelena Marasevic and Clifford Stein and Gil Zussman},
  title =	{{A Fast Distributed Stateless Algorithm for alpha-Fair Packing Problems}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{54:1--54:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6334},
  URN =		{urn:nbn:de:0030-drops-63344},
  doi =		{10.4230/LIPIcs.ICALP.2016.54},
  annote =	{Keywords: Fairness, distributed and stateless algorithms, resource allocation}
}

Keywords: Fairness, distributed and stateless algorithms, resource allocation
Seminar: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 17.08.2016


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