### 抜粋

Mader's disjoint S-paths problem unifies two generalizations of bipartite matching: (a) non-bipartite matching and (b) disjoint s-t paths. Lovász (1980, 1981) first proposed an efficient algorithm for this problem via a reduction to matroid matching, which also unifies two generalizations of bipartite matching: (a) non-bipartite matching and (c) matroid intersection. While the weighted versions of the problems (a)-(c) in which we aim to minimize the total weight of a designated-size feasible solution are known to be solvable in polynomial time, the tractability of such a weighted version of Mader's problem has been open for a long while. In this paper, we present the first solution to this problem with the aid of a linear representation for Lovász' reduction (which leads to a reduction to linear matroid parity) due to Schrijver (2003) and polynomial-time algorithms for a weighted version of linear matroid parity announced by Iwata (2013) and by Pap (2013). Specifically, we give a reduction of the weighted version of Mader's problem to weighted linear matroid parity, which leads to an O(n^{5})-time algorithm for the former problem, where n denotes the number of vertices in the input graph. Our reduction technique is also applicable to a further generalized framework, packing non-zero A-paths in group-labeled graphs, introduced by Chudnovsky, Geelen, Gerards, Goddyn, Lohman, and Seymour (2006). The extension leads to the tractability of a broader class of weighted problems not restricted to Mader's setting.

元の言語 | 英語 |
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ホスト出版物のタイトル | 27th International Symposium on Algorithms and Computation, ISAAC 2016 |

編集者 | Seok-Hee Hong |

出版者 | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

ページ | 63.1-63.13 |

ISBN（電子版） | 9783959770262 |

DOI | |

出版物ステータス | 出版済み - 12 1 2016 |

イベント | 27th International Symposium on Algorithms and Computation, ISAAC 2016 - Sydney, オーストラリア 継続期間: 12 12 2016 → 12 14 2016 |

### 出版物シリーズ

名前 | Leibniz International Proceedings in Informatics, LIPIcs |
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巻 | 64 |

ISSN（印刷物） | 1868-8969 |

### その他

その他 | 27th International Symposium on Algorithms and Computation, ISAAC 2016 |
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国 | オーストラリア |

市 | Sydney |

期間 | 12/12/16 → 12/14/16 |

### All Science Journal Classification (ASJC) codes

- Software

## フィンガープリント Shortest disjoint S-paths via weighted linear matroid parity' の研究トピックを掘り下げます。これらはともに一意のフィンガープリントを構成します。

## これを引用

*27th International Symposium on Algorithms and Computation, ISAAC 2016*(pp. 63.1-63.13). (Leibniz International Proceedings in Informatics, LIPIcs; 巻数 64). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ISAAC.2016.63