Optimal girth approximation for dense directed graphs

Shiri Chechik*, Gur Lifshitz

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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 languageEnglish
Title of host publicationACM-SIAM Symposium on Discrete Algorithms, SODA 2021
EditorsDaniel Marx
PublisherAssociation for Computing Machinery
Pages290-300
Number of pages11
ISBN (Electronic)9781611976465
StatePublished - 2021
Event32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021 - Alexandria, Virtual, United States
Duration: 10 Jan 202113 Jan 2021

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Conference

Conference32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021
Country/TerritoryUnited States
CityAlexandria, Virtual
Period10/01/2113/01/21

Fingerprint

Dive into the research topics of 'Optimal girth approximation for dense directed graphs'. Together they form a unique fingerprint.

Cite this