Packing A-paths in group-labelled graphs via linear matroid parity

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

1 引用 (Scopus)

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
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 20141 7 2014

出版物シリーズ

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

会議

会議25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014
米国
Portland, OR
期間1/5/141/7/14

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

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  • これを引用

    Yamaguchi, Y. (2014). Packing A-paths in group-labelled graphs via linear matroid parity. : 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