A strongly polynomial algorithm for finding a shortest non-zero path in group-labeled graphs

研究成果: 著書/レポートタイプへの貢献会議での発言

抜粋

We study a constrained shortest path problem in group-labeled graphs with nonnegative edge length, called the shortest non-zero path problem. Depending on the group in question, this problem includes two types of tractable variants in undirected graphs: one is the parity-constrained shortest path/cycle problem, and the other is computing a shortest noncontractible cycle in surface-embedded graphs. For the shortest non-zero path problem with respect to finite abelian groups, Kobayashi and Toyooka (2017) proposed a randomized, pseudopolynomial algorithm via permanent computation. For a slightly more general class of groups, Yamaguchi (2016) showed a reduction of the problem to the weighted linear matroid parity problem. In particular, some cases are solved in strongly polynomial time via the reduction with the aid of a deterministic, polynomial algorithm for the weighted linear matroid parity problem developed by Iwata and Kobayashi (2017), which generalizes a well-known fact that the parity-constrained shortest path problem is solved via weighted matching. In this paper, as the first general solution independent of the group, we present a rather simple, deterministic, and strongly polynomial algorithm for the shortest non-zero path problem. The algorithm is based on Dijkstra's algorithm for the unconstrained shortest path problem and Edmonds' blossom shrinking technique in matching algorithms, and clarifies a common tractable feature behind the parity and topological constraints in the shortest path/cycle problem.

元の言語英語
ホスト出版物のタイトル31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020
編集者Shuchi Chawla
出版者Association for Computing Machinery
ページ1923-1932
ページ数10
ISBN(電子版)9781611975994
出版物ステータス出版済み - 1 1 2020
イベント31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020 - Salt Lake City, 米国
継続期間: 1 5 20201 8 2020

出版物シリーズ

名前Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
2020-January

会議

会議31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020
米国
Salt Lake City
期間1/5/201/8/20

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

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  • これを引用

    Yamaguchi, Y. (2020). A strongly polynomial algorithm for finding a shortest non-zero path in group-labeled graphs. : S. Chawla (版), 31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020 (pp. 1923-1932). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms; 巻数 2020-January). Association for Computing Machinery.