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.ITCS.2017.36
URN: urn:nbn:de:0030-drops-81489
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8148/
Anari, Nima ;
Oveis Gharan, Shayan ;
Saberi, Amin ;
Singh, Mohit
Nash Social Welfare, Matrix Permanent, and Stable Polynomials
Abstract
We study the problem of allocating m items to n agents subject to maximizing the Nash social welfare (NSW) objective. We write a novel convex programming relaxation for this problem, and we show that a simple randomized rounding algorithm gives a 1/e approximation factor of the objective, breaking the 1/2e^(1/e) approximation factor of Cole and Gkatzelis.
Our main technical contribution is an extension of Gurvits's lower bound on the coefficient of the square-free monomial of a degree m-homogeneous stable polynomial on m variables to all homogeneous polynomials. We use this extension to analyze the expected welfare of the allocation returned by our randomized rounding algorithm.
BibTeX - Entry
@InProceedings{anari_et_al:LIPIcs:2017:8148,
author = {Nima Anari and Shayan Oveis Gharan and Amin Saberi and Mohit Singh},
title = {{Nash Social Welfare, Matrix Permanent, and Stable Polynomials}},
booktitle = {8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
pages = {36:1--36:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-029-3},
ISSN = {1868-8969},
year = {2017},
volume = {67},
editor = {Christos H. Papadimitriou},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/8148},
URN = {urn:nbn:de:0030-drops-81489},
doi = {10.4230/LIPIcs.ITCS.2017.36},
annote = {Keywords: Nash Welfare, Permanent, Matching, Stable Polynomial, Randomized Algorithm, Saddle Point}
}
Keywords: |
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Nash Welfare, Permanent, Matching, Stable Polynomial, Randomized Algorithm, Saddle Point |
Collection: |
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8th Innovations in Theoretical Computer Science Conference (ITCS 2017) |
Issue Date: |
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2017 |
Date of publication: |
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28.11.2017 |