Optimal Matroid Partitioning Problems

Yasushi Kawase, Kei Kimura, Kazuhisa Makino, Hanna Sumita

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)1653-1676
Number of pages24
JournalAlgorithmica
Volume83
Issue number6
DOIs
Publication statusPublished - Jun 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Computer Science Applications
  • Applied Mathematics

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