A Note on Improved Results for One Round Distributed Clique Listing

by   Quanquan C. Liu, et al.

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.


page 1

page 2

page 3

page 4


Distributed Detection of Cliques in Dynamic Networks

This paper provides an in-depth study of the fundamental problems of fin...

Advice Complexity bounds for Online Delayed F-Node-, H-Node- and H-Edge-Deletion Problems

Let F be a fixed finite obstruction set of graphs and G be a graph revea...

Fast Distributed Vertex Splitting with Applications

We present polyloglog n-round randomized distributed algorithms to compu...

Fast and Simple Deterministic Algorithms for Highly-Dynamic Networks

This paper provides a surprisingly simple method for obtaining fast (con...

Sketch-based Randomized Algorithms for Dynamic Graph Regression

A well-known problem in data science and machine learning is linear reg...

The Predicted-Deletion Dynamic Model: Taking Advantage of ML Predictions, for Free

The main bottleneck in designing efficient dynamic algorithms is the unk...

Please sign up or login with your details

Forgot password? Click here to reset