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A Note on Improved Results for One Round Distributed Clique Listing

Quanquan C. Liu
Dec 2022
摘要
In this note, we investigate listing cliques of arbitrary sizes inbandwidth-limited, dynamic networks. The problem of detecting and listingtriangles and cliques was originally studied in great detail by Bonne andCensor-Hillel (ICALP 2019). We extend this study to dynamic graphs where morethan one update may occur as well as resolve an open question posed by Bonneand Censor-Hillel (2019). Our algorithms and results are based on some simpleobservations about listing triangles under various settings and we show that wecan list larger cliques using such facts. Specifically, we show that ourtechniques can be used to solve an open problem posed in the original paper: weshow that detecting and listing cliques (of any size) can be done using$O(1)$-bandwidth after one round of communication under node insertions andnode/edge deletions. We conclude with an extension of our techniques to obtaina small bandwidth $1$-round algorithm for listing cliques when more than onenode insertion/deletion and/or edge deletion update occurs at any time.
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