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.ICALP.2016.75
URN: urn:nbn:de:0030-drops-62094
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6209/
Go to the corresponding LIPIcs Volume Portal

Friggstad, Zachary ; Zhang, Yifeng

Tight Analysis of a Multiple-Swap Heurstic for Budgeted Red-Blue Median

pdf-format:
LIPIcs-ICALP-2016-75.pdf (0.6 MB)

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: Approximation Algorithms, Local search, Red-Blue Meidan
Collection: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 23.08.2016

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI