Partitioning vectors into quadruples: Worst-case analysis of a matching-based algorithm

Annette M.C. Ficker, Thomas Erlebach, Matúš Mihalák, Frits C.R. Spieksma

Samenvatting

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 2 3 -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.

Originele taal-2 Engels Partitioning Vectors into Quadruples: Worst-Case Analysis of a Matching-Based Algorithm Wen-Lian Hsu, Der-Tsai Lee, Chung-Shou Liao Wadern Schloss Dagstuhl - Leibniz-Zentrum für Informatik 12 9783959770941 https://doi.org/10.4230/LIPIcs.ISAAC.2018.45 Gepubliceerd - 1 dec 2018 29th International Symposium on Algorithms and Computation, ISAAC 2018 - Hotel Royal Chiaohsi, Jiaoxi, Yilan, TaiwanDuur: 16 dec 2018 → 19 dec 2018

Publicatie series

Naam Leibniz International Proceedings in Informatics (LIPIcs) 123 1868-8969

Congres

Congres 29th International Symposium on Algorithms and Computation, ISAAC 2018 Taiwan Jiaoxi, Yilan 16/12/18 → 19/12/18