Optimal Matroid Partitioning Problems

Yasushi Kawase, Kei Kimura, Kazuhisa Makino, Hanna Sumita

研究成果: Contribution to journalArticle査読

抄録

This paper studies optimal matroid partitioning problems for various objective functions. In the problem, we are given k weighted-matroids on the same ground set. Our goal is to find a feasible partition that minimizes (maximizes) the value of an objective function. A typical objective is the maximum over all subsets of the total weights of the elements in a subset, which is extensively studied in the scheduling literature. Likewise, as an objective function, we handle the maximum/minimum/sum over all subsets of the maximum/minimum/total weight(s) of the elements in a subset. In this paper, we determine the computational complexity of the optimal partitioning problem with the above-described objective functions. Namely, for each objective function, we either provide a polynomial time algorithm or prove NP-hardness. We also discuss the approximability for the NP-hard cases.

本文言語英語
ページ(範囲)1653-1676
ページ数24
ジャーナルAlgorithmica
83
6
DOI
出版ステータス出版済み - 6 2021
外部発表はい

All Science Journal Classification (ASJC) codes

  • コンピュータ サイエンス(全般)
  • コンピュータ サイエンスの応用
  • 応用数学

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