Improved girth approximation in weighted undirected graphs

Avi Kadria; Liam Roditty; Aaron Sidford; Virginia Vassilevska Williams; Uri Zwick

Improved girth approximation in weighted undirected graphs

Avi Kadria, Liam Roditty, Aaron Sidford, Virginia Vassilevska Williams, Uri Zwick

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

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
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
Volume	2023-January

Conference

Conference	34th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2023
Country/Territory	Italy
City	Florence
Period	22/01/23 → 25/01/23

Bibliographical note

Publisher Copyright:
Copyright © 2023 by SIAM.

Funding

∗Department of Computer Science, Bar Ilan University, Ramat Gan 5290002, Israel. E-mail [email protected]. †Department of Computer Science, Bar Ilan University, Ramat Gan 5290002, Israel. E-mail [email protected]. Supported in part by BSF grants 2016365 and 2020356. ‡Departments of Management Science and Engineering and Computer Science, Stanford University, Stanford, CA, 94305, USA. E-mail [email protected]. Supported in part by BSF grant no. 2016365, a Microsoft Research Faculty Fellowship, NSF CAREER Award CCF-1844855, NSF Grant CCF-1955039, a PayPal research award, and a Sloan Research Fellowship §Department of Electrical Engineering and Computer Science and CSAIL, MIT, Cambridge, MA, USA. E-mail [email protected]. Supported in part by NSF CAREER Award 1651838, NSF Grants CCF-1909429 and CCF-2129139, BSF grants 2016365 and 2020356, a Google Research Fellowship and a Sloan Research Fellowship. ¶Blavatnik School of Computer Science, Tel Aviv University, Tel Aviv 6997801, Israel. E-mail [email protected]. Supported in part by BSF grants 2016365 and 2020356. 1Õ(f(n)) denotes O(f(n)polylog(n)).

Funders	Funder number
National Science Foundation	CCF-1909429, CCF-1955039, CCF-2129139, 1651838, CCF-1844855
Microsoft Research
Google
Massachusetts Institute of Technology
Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology
United States-Israel Binational Science Foundation	2016365, 2020356

Cite this

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title = "Improved girth approximation in weighted undirected graphs",

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(kn1+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((n1+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].",

author = "Avi Kadria and Liam Roditty and Aaron Sidford and Williams, \{Virginia Vassilevska\} and Uri Zwick",

note = "Publisher Copyright: Copyright {\textcopyright} 2023 by SIAM.; 34th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2023 ; Conference date: 22-01-2023 Through 25-01-2023",

year = "2023",

language = "אנגלית",

series = "Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms",

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booktitle = "34th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2023",

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Kadria, A, Roditty, L, Sidford, A, Williams, VV & Zwick, U 2023, Improved girth approximation in weighted undirected graphs. in 34th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2023. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 2023-January, Association for Computing Machinery, pp. 2242-2255, 34th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2023, Florence, Italy, 22/01/23.

Improved girth approximation in weighted undirected graphs. / Kadria, Avi; Roditty, Liam; Sidford, Aaron et al.
34th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2023. Association for Computing Machinery, 2023. p. 2242-2255 (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms; Vol. 2023-January).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - 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(kn1+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((n1+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].

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Improved girth approximation in weighted undirected graphs

Abstract

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Bibliographical note

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