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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2016.23
URN: urn:nbn:de:0030-drops-67939
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6793/
Chan, T-H. Hubert ;
Tang, Zhihao Gavin ;
Wu, Xiaowei
On (1, epsilon)-Restricted Max-Min Fair Allocation Problem
Abstract
We study the max-min fair allocation problem in which a set of m indivisible items are to be distributed among n agents such that the minimum utility among all agents is maximized. In the restricted setting, the utility of each item j on agent i is either 0 or some non-negative weight w_j. For this setting, Asadpour et al. [TALG, 2012] showed that a certain configuration-LP can be used to estimate the optimal value within a factor of 4 + delta, for any delta > 0, which was recently extended by Annamalai et al. [SODA 2015] to give a polynomial-time 13-approximation algorithm for the problem. For hardness results, Bezáková and Dani [SIGecom Exch., 2005] showed that it is NP-hard to approximate the problem within any ratio smaller than 2.
In this paper we consider the (1, epsilon)-restricted max-min fair allocation problem, in which for some parameter epsilon in (0, 1), each item j is either heavy (w_j = 1) or light (w_j = epsilon). We show that the (1, epsilon)-restricted case is also NP-hard to approximate within any ratio smaller than 2. Hence, this simple special case is still algorithmically interesting.
Using the configuration-LP, we are able to estimate the optimal value of the problem within a factor of 3 + delta, for any delta > 0. Extending this idea, we also obtain a quasi-polynomial time (3 + 4 epsilon)-approximation algorithm and a polynomial time 9-approximation algorithm. Moreover, we show that as epsilon tends to 0, the approximation ratio of our polynomial-time algorithm approaches 3 + 2 sqrt{2} approx 5.83.
BibTeX - Entry
@InProceedings{chan_et_al:LIPIcs:2016:6793,
author = {T-H. Hubert Chan and Zhihao Gavin Tang and Xiaowei Wu},
title = {{On (1, epsilon)-Restricted Max-Min Fair Allocation Problem}},
booktitle = {27th International Symposium on Algorithms and Computation (ISAAC 2016)},
pages = {23:1--23:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-026-2},
ISSN = {1868-8969},
year = {2016},
volume = {64},
editor = {Seok-Hee Hong},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/6793},
URN = {urn:nbn:de:0030-drops-67939},
doi = {10.4230/LIPIcs.ISAAC.2016.23},
annote = {Keywords: Max-Min Fair Allocation, Hypergraph Matching}
}
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Keywords: |
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Max-Min Fair Allocation, Hypergraph Matching |
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Collection: |
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27th International Symposium on Algorithms and Computation (ISAAC 2016) |
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Issue Date: |
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2016 |
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Date of publication: |
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07.12.2016 |
