Algorithmic trade-offs for girth approximation in undirected graphs

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

Algorithmic trade-offs for girth approximation in 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

4 Scopus citations

Abstract

We present several new effcient algorithms for approximating the girth, g, of weighted and unweighted n-vertex, m-edge undirected graphs. For undirected graphs with polynomially bounded, integer, non-negative edge weights, we provide an algorithm that for every integer k 1, runs in eO(m + n1+1=k log g) time and returns a cycle of length at most 2kg. For unweighted, undirected graphs we present an algorithm that for every k 1, runs in eO (n1+1=k) time and returns a cycle of length at most 2kdg=2e, an almost k-approximation. Both algorithms provide trade-off-s between the running time and the quality of the approximation. We also obtain faster algorithms for approximation factors better than 2, and improved approximations when the girth is odd or small (e.g., 3 and 4).

Original language	English
Title of host publication	ACM-SIAM Symposium on Discrete Algorithms, SODA 2022
Publisher	Association for Computing Machinery
Pages	1471-1492
Number of pages	22
ISBN (Electronic)	9781611977073
State	Published - 2022
Event	33rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2022 - Alexander, United States Duration: 9 Jan 2022 → 12 Jan 2022

Publication series

Name	Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume	2022-January

Conference

Conference	33rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2022
Country/Territory	United States
City	Alexander
Period	9/01/22 → 12/01/22

Bibliographical note

Publisher Copyright:
Copyright © 2022 by SIAM Unauthorized reproduction of this article is prohibited.

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.

Funders	Funder number
National Science Foundation	CCF-1955039, CCF-1844855
Microsoft Research
Google
Massachusetts Institute of Technology	CCF-1909429, CCF-2129139, 1651838
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 = "Algorithmic trade-offs for girth approximation in undirected graphs",

abstract = "We present several new effcient algorithms for approximating the girth, g, of weighted and unweighted n-vertex, m-edge undirected graphs. For undirected graphs with polynomially bounded, integer, non-negative edge weights, we provide an algorithm that for every integer k 1, runs in eO(m + n1+1=k log g) time and returns a cycle of length at most 2kg. For unweighted, undirected graphs we present an algorithm that for every k 1, runs in eO (n1+1=k) time and returns a cycle of length at most 2kdg=2e, an almost k-approximation. Both algorithms provide trade-off-s between the running time and the quality of the approximation. We also obtain faster algorithms for approximation factors better than 2, and improved approximations when the girth is odd or small (e.g., 3 and 4).",

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

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year = "2022",

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Kadria, A, Roditty, L, Sidford, A, Williams, VV & Zwick, U 2022, Algorithmic trade-offs for girth approximation in undirected graphs. in ACM-SIAM Symposium on Discrete Algorithms, SODA 2022. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 2022-January, Association for Computing Machinery, pp. 1471-1492, 33rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2022, Alexander, United States, 9/01/22.

Algorithmic trade-offs for girth approximation in undirected graphs. / Kadria, Avi; Roditty, Liam; Sidford, Aaron et al.
ACM-SIAM Symposium on Discrete Algorithms, SODA 2022. Association for Computing Machinery, 2022. p. 1471-1492 (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms; Vol. 2022-January).

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

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AB - We present several new effcient algorithms for approximating the girth, g, of weighted and unweighted n-vertex, m-edge undirected graphs. For undirected graphs with polynomially bounded, integer, non-negative edge weights, we provide an algorithm that for every integer k 1, runs in eO(m + n1+1=k log g) time and returns a cycle of length at most 2kg. For unweighted, undirected graphs we present an algorithm that for every k 1, runs in eO (n1+1=k) time and returns a cycle of length at most 2kdg=2e, an almost k-approximation. Both algorithms provide trade-off-s between the running time and the quality of the approximation. We also obtain faster algorithms for approximation factors better than 2, and improved approximations when the girth is odd or small (e.g., 3 and 4).

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Algorithmic trade-offs for girth approximation in undirected graphs

Abstract

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Bibliographical note

Funding

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