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DOI: 10.4230/LIPIcs.ISAAC.2017.51
URN: urn:nbn:de:0030-drops-82712
URL: https://drops.dagstuhl.de/opus/volltexte/2017/8271/
Kawase, Yasushi ; Kimura, Kei ; Makino, Kazuhisa ; Sumita, Hanna
Optimal Matroid Partitioning Problems
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Abstract
This paper studies optimal matroid partitioning problems for various objective functions. In the problem, we are given a finite set E and k weighted matroids (E, \mathcal{I}_i, w_i), i = 1, \dots, k, and our task is to find a minimum partition (I_1,\dots,I_k) of E such that I_i \in \mathcal{I}_i for all i. For each objective function, we give a polynomial-time algorithm or prove NP-hardness. In particular, for the case when the given weighted matroids are identical and the objective function is the sum of the maximum weight in each set (i.e., \sum_{i=1}^k\max_{e\in I_i}w_i(e)), we show that the problem is strongly NP-hard but admits a PTAS.
BibTeX - Entry
@InProceedings{kawase_et_al:LIPIcs:2017:8271,
author = {Yasushi Kawase and Kei Kimura and Kazuhisa Makino and Hanna Sumita},
title = {{Optimal Matroid Partitioning Problems}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {51:1--51:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Yoshio Okamoto and Takeshi Tokuyama},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/8271},
URN = {urn:nbn:de:0030-drops-82712},
doi = {10.4230/LIPIcs.ISAAC.2017.51},
annote = {Keywords: Matroids, Partitioning problem, PTAS, NP-hardness}
}
| Keywords: | Matroids, Partitioning problem, PTAS, NP-hardness | |
| Seminar: | 28th International Symposium on Algorithms and Computation (ISAAC 2017) | |
| Issue date: | 2017 | |
| Date of publication: | 07.12.2017 |
