@inproceedings{918378fa74f94ac3bc722890e24d38aa,
title = "Partitioning Vectors into Quadruples: Worst-Case Analysis of a Matching-Based Algorithm",
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 23 -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 54 -approximation algorithm. Our analysis is tight in all cases except one.",
author = "Ficker, {Annette M. C.} and Thomas Erlebach and Mat{\'u}s Mihal{\'a}k and Spieksma, {Frits C. R.}",
year = "2018",
doi = "10.4230/LIPIcs.ISAAC.2018.45",
language = "English",
isbn = "978-3-95977-094-1",
volume = "123",
series = "Leibniz International Proceedings in Informatics",
publisher = "Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik",
pages = "45:1--45:12",
editor = "Wen-Lian Hsu and Der-Tsai Lee and Chung-Shou Liao",
booktitle = "29th International Symposium on Algorithms and Computation (ISAAC 2018)",
address = "Germany",
}