### 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 |
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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 2020 → 1 8 2020 |

### 出版物シリーズ

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

### 会議

会議 | 31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020 |
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国 | 米国 |

市 | Salt Lake City |

期間 | 1/5/20 → 1/8/20 |

### All Science Journal Classification (ASJC) codes

- Software
- Mathematics(all)

## フィンガープリント A strongly polynomial algorithm for finding a shortest non-zero path in group-labeled graphs' 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

*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.