文章基本信息

标题：Optimal Matroid Partitioning Problems
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作者：Yasushi Kawase ; Kei Kimura ; Kazuhisa Makino 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2017
卷号：92
页码：51:1-51:13
DOI：10.4230/LIPIcs.ISAAC.2017.51
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：Matroids; Partitioning problem; PTAS; NP-hardness