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.2017.51
URN: urn:nbn:de:0030-drops-82712
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8271/
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Kawase, Yasushi ; Kimura, Kei ; Makino, Kazuhisa ; Sumita, Hanna

Optimal Matroid Partitioning Problems

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LIPIcs-ISAAC-2017-51.pdf (0.6 MB)

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
Collection: 28th International Symposium on Algorithms and Computation (ISAAC 2017)
Issue Date: 2017
Date of publication: 07.12.2017

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