### 抜粋

Mader's disjoint 5-paths problem is a common generalization of non-bipartite matching and Menger's disjoint paths problems. Lovasz (1980) suggested a polynomial-time algorithm for this problem through a reduction to matroid matching. A more direct reduction to the linear matroid parity problem was given later by Schrijver (2003), which leads to faster algorithms. As a generalization of Mader's problem, Chudnovsky, Geelen, Gerards, Goddyn, Lohman, and Seymour (2006) introduced a framework of packing non-zero A-paths in group-labelled graphs, and proved a min-max theorem. Chudnovsky, Cunningham, and Geelen (2008) provided an efficient combinatorial algorithm for this generalized problem. On the other hand, Pap (2007) introduced a framework of packing non-returning A-paths as a further genaralization. In this paper, we discuss a possible extension of Schri- jver's reduction technique to another framework introduced by Pap (2006), under the name of the subgroup model, which apparently generalizes but in fact is equivalent to packing non-returning .A-paths. We provide a necessary and sufficient condition for the groups in question to admit a reduction to the linear matroid parity problem. As a consequence, we give faster algorithms for important special cases of packing non-zero A-paths such as odd-length .4-paths. In addition, it turns out that packing non-returning A-paths admits a reduction to the linear matroid parity problem, which leads to the quite efficient solvability, if and only if the size of the input label set is at most four.

元の言語 | 英語 |
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ホスト出版物のタイトル | Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014 |

出版者 | Association for Computing Machinery |

ページ | 562-569 |

ページ数 | 8 |

ISBN（印刷物） | 9781611973389 |

DOI | |

出版物ステータス | 出版済み - 2014 |

外部発表 | Yes |

イベント | 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014 - Portland, OR, 米国 継続期間: 1 5 2014 → 1 7 2014 |

### 出版物シリーズ

名前 | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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### 会議

会議 | 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014 |
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国 | 米国 |

市 | Portland, OR |

期間 | 1/5/14 → 1/7/14 |

### All Science Journal Classification (ASJC) codes

- Software
- Mathematics(all)

## フィンガープリント Packing A-paths in group-labelled graphs via 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

*Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014*(pp. 562-569). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms). Association for Computing Machinery. https://doi.org/10.1137/1.9781611973402.42