Massively Parallel Correlation Clustering in Bounded Arboricity Graphs

Melanie Cambus, Davin Choo, Havu Miikonen, Jara Uitto

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

8 Citations (Scopus)
31 Downloads (Pure)

Abstract

Identifying clusters of similar elements in a set is a common task in data analysis. With the immense growth of data and physical limitations on single processor speed, it is necessary to find efficient parallel algorithms for clustering tasks. In this paper, we study the problem of correlation clustering in bounded arboricity graphs with respect to the Massively Parallel Computation (MPC) model. More specifically, we are given a complete graph where the edges are either positive or negative, indicating whether pairs of vertices are similar or dissimilar. The task is to partition the vertices into clusters with as few disagreements as possible. That is, we want to minimize the number of positive inter-cluster edges and negative intra-cluster edges.
Consider an input graph G on n vertices such that the positive edges induce a λ-arboric graph. Our main result is a 3-approximation (in expectation) algorithm to correlation clustering that runs in 𝒪(log λ ⋅ poly(log log n)) MPC rounds in the strongly sublinear memory regime. This is obtained by combining structural properties of correlation clustering on bounded arboricity graphs with the insights of Fischer and Noever (SODA '18) on randomized greedy MIS and the PIVOT algorithm of Ailon, Charikar, and Newman (STOC '05). Combined with known graph matching algorithms, our structural property also implies an exact algorithm and algorithms with worst case (1+ε)-approximation guarantees in the special case of forests, where λ = 1.
Original languageEnglish
Title of host publication35th International Symposium on Distributed Computing, DISC 2021
EditorsSeth Gilbert
PublisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik
Number of pages18
ISBN (Electronic)978-3-95977-210-5
DOIs
Publication statusPublished - 2021
MoE publication typeA4 Conference publication
EventInternational Symposium on Distributed Computing - Virtual, Online, Freiburg, Germany
Duration: 4 Oct 20218 Oct 2021
Conference number: 35

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Volume209
ISSN (Electronic)1868-8969

Conference

ConferenceInternational Symposium on Distributed Computing
Abbreviated titleDISC
Country/TerritoryGermany
CityFreiburg
Period04/10/202108/10/2021

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