Listing 4-Cycles

Amir Abboud, Seri Khoury, Oree Leibowitz, Ron Safier

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

Abstract

We study the fine-grained complexity of listing all 4-cycles in a graph on n nodes, m edges, and t such 4-cycles. The main result is an Õ (min(n2,m4/3) + t) upper bound, which is best-possible up to log factors unless the long-standing O(min(n2,m4/3)) upper bound for detecting a 4-cycle can be broken. Moreover, it almost-matches recent 3-SUM-based lower bounds for the problem by Abboud, Bringmann, and Fischer (STOC 2023) and independently by Jin and Xu (STOC 2023). Notably, our result separates 4-cycle listing from the closely related triangle listing for which higher conditional lower bounds exist, and rule out such a "detection plus t" bound. We also show by simple arguments that our bound cannot be extended to mild generalizations of the problem such as reporting all pairs of nodes that participate in a 4-cycle. Independent work: Jin and Xu [26] also present an algorithm with the same time bound.

Original languageEnglish
Title of host publication43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2023
EditorsPatricia Bouyer, Srikanth Srinivasan
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959773041
DOIs
StatePublished - Dec 2023
Event43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2023 - Hyderabad, India
Duration: 18 Dec 202320 Dec 2023

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume284
ISSN (Print)1868-8969

Conference

Conference43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2023
Country/TerritoryIndia
CityHyderabad
Period18/12/2320/12/23

All Science Journal Classification (ASJC) codes

  • Software

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