Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Gupta, Anupam; Moseley, Benjamin; Zhou, Rudy https://www.dagstuhl.de/lipics License: Creative Commons Attribution 4.0 license (CC BY 4.0)
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URN: urn:nbn:de:0030-drops-141465
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Structural Iterative Rounding for Generalized k-Median Problems

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Abstract

This paper considers approximation algorithms for generalized k-median problems. This class of problems can be informally described as k-median with a constant number of extra constraints, and includes k-median with outliers, and knapsack median. Our first contribution is a pseudo-approximation algorithm for generalized k-median that outputs a 6.387-approximate solution with a constant number of fractional variables. The algorithm is based on iteratively rounding linear programs, and the main technical innovation comes from understanding the rich structure of the resulting extreme points.
Using our pseudo-approximation algorithm, we give improved approximation algorithms for k-median with outliers and knapsack median. This involves combining our pseudo-approximation with pre- and post-processing steps to round a constant number of fractional variables at a small increase in cost. Our algorithms achieve approximation ratios 6.994 + ε and 6.387 + ε for k-median with outliers and knapsack median, respectively. These both improve on the best known approximations.

BibTeX - Entry

@InProceedings{gupta_et_al:LIPIcs.ICALP.2021.77,
  author =	{Gupta, Anupam and Moseley, Benjamin and Zhou, Rudy},
  title =	{{Structural Iterative Rounding for Generalized k-Median Problems}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{77:1--77:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14146},
  URN =		{urn:nbn:de:0030-drops-141465},
  doi =		{10.4230/LIPIcs.ICALP.2021.77},
  annote =	{Keywords: approximation algorithms, clustering, linear programming}
}

Keywords: approximation algorithms, clustering, linear programming
Seminar: 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Issue date: 2021
Date of publication: 02.07.2021


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