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://drops.dagstuhl.de/opus/volltexte/2017/8271/
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### 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},