Shortest disjoint S-paths via weighted linear matroid parity

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

1 引用 (Scopus)

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(n5)-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
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 201612 14 2016

出版物シリーズ

名前Leibniz International Proceedings in Informatics, LIPIcs
64
ISSN(印刷物)1868-8969

その他

その他27th International Symposium on Algorithms and Computation, ISAAC 2016
オーストラリア
Sydney
期間12/12/1612/14/16

All Science Journal Classification (ASJC) codes

  • Software

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  • これを引用

    Yamaguchi, Y. (2016). Shortest disjoint S-paths via weighted linear matroid parity. : S-H. Hong (版), 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