A note on improved results for one round distributed clique listing

In this note, we investigate listing cliques of arbitrary sizes in bandwidth-limited, dynamic networks. The problem of detecting and listing triangles and cliques was originally studied in great detail by Bonne and Censor-Hillel (ICALP 2019). We extend this study to dynamic graphs where more than on...

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Bibliographic Details
Published in:Information processing letters Vol. 181; p. 106355
Main Author: Liu, Quanquan C.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.03.2023
Subjects:
Clique counting
Distributed algorithms
Dynamic algorithms
Graph algorithms
Triangle counting
Dynamic algorithms
Graph algorithms
Clique counting
Triangle counting
Distributed algorithms
ISSN:0020-0190, 1872-6119
Online Access:Get full text
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Summary:In this note, we investigate listing cliques of arbitrary sizes in bandwidth-limited, dynamic networks. The problem of detecting and listing triangles and cliques was originally studied in great detail by Bonne and Censor-Hillel (ICALP 2019). We extend this study to dynamic graphs where more than one update may occur as well as resolve an open question posed by Bonne and Censor-Hillel (2019). Our algorithms and results are based on some simple observations about listing triangles under various settings and we show that we can list larger cliques using such facts. Specifically, we show that our techniques can be used to solve an open problem posed in the original paper: we show that detecting and listing cliques (of any size) can be done using O(1)-bandwidth after one round of communication under node insertions and node/edge deletions. We conclude with an extension of our techniques to obtain a small bandwidth 1-round algorithm for listing cliques when more than one node insertion/deletion and/or edge deletion update occurs at any time. •We investigate 1-round clique listing in bandwidth-limited, dynamic networks in the CONGEST model.•We present an O(1)-bandwidth, 1-round algorithm for listing k-cliques under node insertions/deletions and edge deletions.•Our algorithm improves on the state-of-the-art from O(log⁡n) bandwidth to O(1).•We extend our results to multiple simultaneous updates.•Our paper is the first to study multiple simultaneous updates in the 1-round, bandwidth- limited setting.
ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2022.106355