Optimal girth approximation for dense directed graphs

Shiri Chechik; Gur Lifshitz

doi:10.1137/1.9781611976465.19

Optimal girth approximation for dense directed graphs

Shiri Chechik^*, Gur Lifshitz

^*Corresponding author for this work

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

6 Scopus citations

Abstract

In this paper we provide a Õ(n²) time algorithm that computes a 2-multiplicative approximation of the girth of an n-node m-edge directed graph with non-negative edge weights. We also provide an additional algorithm that computes a 2-multiplicative approximation of the girth in Õ(m√n) time ¹. Our results naturally provide algorithms for improved constructions of 4-roundtrip spanners, the analog of spanners in directed graphs. Our algorithm is optimal (up to a log n factor) for dense graphs with m = Θ(n²). For comparison, previously, the best approximation ratio with a similar running time for dense graphs was O(log n log log n) [1]. Moreover, unlike previous algorithms, our algorithm neither assumes integer weights, nor does it depend on the maximum edge weight of the graph.

Original language	English
Title of host publication	ACM-SIAM Symposium on Discrete Algorithms, SODA 2021
Editors	Daniel Marx
Publisher	Association for Computing Machinery
Pages	290-300
Number of pages	11
ISBN (Electronic)	9781611976465
DOIs	https://doi.org/10.1137/1.9781611976465.19
State	Published - 2021
Event	32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021 - Alexandria, Virtual, United States Duration: 10 Jan 2021 → 13 Jan 2021

Publication series

Name	Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
ISSN (Print)	1071-9040
ISSN (Electronic)	1557-9468

Conference

Conference	32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021
Country/Territory	United States
City	Alexandria, Virtual
Period	10/01/21 → 13/01/21

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10.1137/1.9781611976465.19

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title = "Optimal girth approximation for dense directed graphs",

abstract = "In this paper we provide a {\~O}(n2) time algorithm that computes a 2-multiplicative approximation of the girth of an n-node m-edge directed graph with non-negative edge weights. We also provide an additional algorithm that computes a 2-multiplicative approximation of the girth in {\~O}(m√n) time 1. Our results naturally provide algorithms for improved constructions of 4-roundtrip spanners, the analog of spanners in directed graphs. Our algorithm is optimal (up to a log n factor) for dense graphs with m = Θ(n2). For comparison, previously, the best approximation ratio with a similar running time for dense graphs was O(log n log log n) [1]. Moreover, unlike previous algorithms, our algorithm neither assumes integer weights, nor does it depend on the maximum edge weight of the graph.",

author = "Shiri Chechik and Gur Lifshitz",

note = "Publisher Copyright: Copyright {\textcopyright} 2021 by SIAM; 32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021 ; Conference date: 10-01-2021 Through 13-01-2021",

year = "2021",

doi = "10.1137/1.9781611976465.19",

language = "אנגלית",

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

publisher = "Association for Computing Machinery",

pages = "290--300",

editor = "Daniel Marx",

booktitle = "ACM-SIAM Symposium on Discrete Algorithms, SODA 2021",

address = "ארצות הברית",

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Chechik, S & Lifshitz, G 2021, Optimal girth approximation for dense directed graphs. in D Marx (ed.), ACM-SIAM Symposium on Discrete Algorithms, SODA 2021. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, Association for Computing Machinery, pp. 290-300, 32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021, Alexandria, Virtual, United States, 10/01/21. https://doi.org/10.1137/1.9781611976465.19

Optimal girth approximation for dense directed graphs. / Chechik, Shiri; Lifshitz, Gur.
ACM-SIAM Symposium on Discrete Algorithms, SODA 2021. ed. / Daniel Marx. Association for Computing Machinery, 2021. p. 290-300 (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms).

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

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Optimal girth approximation for dense directed graphs

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