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.2019.38
URN: urn:nbn:de:0030-drops-106143
URL: https://drops.dagstuhl.de/opus/volltexte/2019/10614/
Cheng, Siu-Wing ; Mao, Yuchen
Restricted Max-Min Allocation: Approximation and Integrality Gap
| pdf-format: |
|
Abstract
Asadpour, Feige, and Saberi proved that the integrality gap of the configuration LP for the restricted max-min allocation problem is at most 4. However, their proof does not give a polynomial-time approximation algorithm. A lot of efforts have been devoted to designing an efficient algorithm whose approximation ratio can match this upper bound for the integrality gap. In ICALP 2018, we present a (6 + delta)-approximation algorithm where delta can be any positive constant, and there is still a gap of roughly 2. In this paper, we narrow the gap significantly by proposing a (4+delta)-approximation algorithm where delta can be any positive constant. The approximation ratio is with respect to the optimal value of the configuration LP, and the running time is poly(m,n)* n^{poly(1/(delta))} where n is the number of players and m is the number of resources. We also improve the upper bound for the integrality gap of the configuration LP to 3 + 21/26 =~ 3.808.
BibTeX - Entry
@InProceedings{cheng_et_al:LIPIcs:2019:10614,
author = {Siu-Wing Cheng and Yuchen Mao},
title = {{Restricted Max-Min Allocation: Approximation and Integrality Gap}},
booktitle = {46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
pages = {38:1--38:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-109-2},
ISSN = {1868-8969},
year = {2019},
volume = {132},
editor = {Christel Baier and Ioannis Chatzigiannakis and Paola Flocchini and Stefano Leonardi},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/10614},
URN = {urn:nbn:de:0030-drops-106143},
doi = {10.4230/LIPIcs.ICALP.2019.38},
annote = {Keywords: fair allocation, configuration LP, approximation, integrality gap}
}
| Keywords: | fair allocation, configuration LP, approximation, integrality gap | |
| Seminar: | 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019) | |
| Issue date: | 2019 | |
| Date of publication: | 04.07.2019 |
