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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.2016.75
URN: urn:nbn:de:0030-drops-62094
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6209/
Friggstad, Zachary ;
Zhang, Yifeng
Tight Analysis of a Multiple-Swap Heurstic for Budgeted Red-Blue Median
Abstract
Budgeted Red-Blue Median is a generalization of classic k-Median in that there are two sets of facilities, say R and B, that can be used to serve clients located in some metric space. The goal is to open kr facilities in R and kb facilities in B for some given bounds kr, kb and connect each client to their nearest open facility in a way that minimizes the total connection cost.
We extend work by Hajiaghayi, Khandekar, and Kortsarz [2012] and show that a multipleswap local search heuristic can be used to obtain a (5 + epsilon)-approximation for Budgeted RedBlue Median for any constant epsilon > 0. This is an improvement over their single swap analysis and beats the previous best approximation guarantee of 8 by Swamy [2014].
We also present a matching lower bound showing that for every p >= 1, there are instances of Budgeted Red-Blue Median with local optimum solutions for the p-swap heuristic whose cost is 5 + Omega(1/p) times the optimum solution cost. Thus, our analysis is tight up to the lower order terms. In particular, for any epsilon > 0 we show the single-swap heuristic admits local optima whose cost can be as bad as 7 - epsilon times the optimum solution cost.
BibTeX - Entry
@InProceedings{friggstad_et_al:LIPIcs:2016:6209,
author = {Zachary Friggstad and Yifeng Zhang},
title = {{Tight Analysis of a Multiple-Swap Heurstic for Budgeted Red-Blue Median}},
booktitle = {43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
pages = {75:1--75:13},
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/2016/6209},
URN = {urn:nbn:de:0030-drops-62094},
doi = {10.4230/LIPIcs.ICALP.2016.75},
annote = {Keywords: Approximation Algorithms, Local search, Red-Blue Meidan}
}
Keywords: |
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Approximation Algorithms, Local search, Red-Blue Meidan |
Collection: |
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43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016) |
Issue Date: |
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2016 |
Date of publication: |
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23.08.2016 |