## Abstract

Let G = (V, E, ℓ) be a n-nodes m-edges weighted undirected graph, where ℓ : E → (0, ∞) is a real length function defined on its edges. Let g be the length of the shortest cycle in G. We present an algorithm that in O(kn^{1+1/k} log n + m(k + log n)) expected running time finds a cycle of length at most 4k/3 g, for every integer k ≥ 1. This improves upon the previous best algorithm that in O((n^{1+1/k} log n+ m) log(nM)) time, where ℓ : E → [1, M] is an integral length function, finds a cycle of length at most 2kg [KRS^{+}22]. For k = 1 our algorithm also improves the result of Roditty and Tov [RT13].

Original language | English |
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Title of host publication | 34th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2023 |

Publisher | Association for Computing Machinery |

Pages | 2242-2255 |

Number of pages | 14 |

ISBN (Electronic) | 9781611977554 |

State | Published - 2023 |

Event | 34th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2023 - Florence, Italy Duration: 22 Jan 2023 → 25 Jan 2023 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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Volume | 2023-January |

### Conference

Conference | 34th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2023 |
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Country/Territory | Italy |

City | Florence |

Period | 22/01/23 → 25/01/23 |

### Bibliographical note

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