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DOI: 10.4230/LIPIcs.ISAAC.2018.45
URN: urn:nbn:de:0030-drops-99933
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9993/
Ficker, Annette M. C. ; Erlebach, Thomas ; Mihalák, Matús ; Spieksma, Frits C. R.
Partitioning Vectors into Quadruples: Worst-Case Analysis of a Matching-Based Algorithm
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Abstract
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
@InProceedings{ficker_et_al:LIPIcs:2018:9993,
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 = {http://drops.dagstuhl.de/opus/volltexte/2018/9993},
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 | |
| Seminar: | 29th International Symposium on Algorithms and Computation (ISAAC 2018) | |
| Issue date: | 2018 | |
| Date of publication: | 06.12.2018 |
