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.ISAAC.2018.45
URN: urn:nbn:de:0030-drops-99933
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Ficker, Annette M. C. ; Erlebach, Thomas ; Mihalák, Matús ; Spieksma, Frits C. R.

Partitioning Vectors into Quadruples: Worst-Case Analysis of a Matching-Based Algorithm

LIPIcs-ISAAC-2018-45.pdf (0.4 MB)


Consider a problem where 4k given vectors need to be partitioned into k clusters of four vectors each. A cluster of four vectors is called a quad, and the cost of a quad is the sum of the component-wise maxima of the four vectors in the quad. The problem is to partition the given 4k vectors into k quads with minimum total cost. We analyze a straightforward matching-based algorithm and prove that this algorithm is a 3/2-approximation algorithm for this problem. We further analyze the performance of this algorithm on a hierarchy of special cases of the problem and prove that, in one particular case, the algorithm is a 5/4-approximation algorithm. Our analysis is tight in all cases except one.

BibTeX - Entry

  author =	{Annette M. C. Ficker and Thomas Erlebach and Mat{\'u}s Mihal{\'a}k and Frits C. R. Spieksma},
  title =	{{Partitioning Vectors into Quadruples: Worst-Case Analysis of a Matching-Based Algorithm}},
  booktitle =	{29th International Symposium on Algorithms and Computation  (ISAAC 2018)},
  pages =	{45:1--45:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Wen-Lian Hsu and Der-Tsai Lee and Chung-Shou Liao},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-99933},
  doi =		{10.4230/LIPIcs.ISAAC.2018.45},
  annote =	{Keywords: approximation algorithm, matching, clustering problem}

Keywords: approximation algorithm, matching, clustering problem
Collection: 29th International Symposium on Algorithms and Computation (ISAAC 2018)
Issue Date: 2018
Date of publication: 06.12.2018

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