Cliques and clique-like subgraphs (e.g., quasi-cliques) are important dense structures whose counting or listing are essential in applications like complex network analysis and community detection. These problems are usually solved by divide and conquer, where a task over a big graph can be recursively divided into subtasks over smaller subgraphs whose search spaces are disjoint. This divisible algorithmic paradigm brings enormous potential for parallelism, since different subtasks can run concurrently to drastically reduce the overall running time.
In this paper, we explore this potential by proposing a unified framework for counting and listing clique-like subgraphs. We study how to divide and distribute the counting and listing tasks, and meanwhile, to balance the assigned workloads of each thread dynamically. Four applications are studied under our parallel framework, i.e., triangle counting, clique counting, maximal clique listing and quasi-clique listing. Extensive experiments are conducted which demonstrate that our solution achieves an ideal speedup on various real graph datasets.
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This content will become publicly available on June 10, 2025
Towards Optimal Output-Sensitive Clique Listing or: Listing Cliques from Smaller Cliques
- Award ID(s):
- 2330048
- NSF-PAR ID:
- 10524474
- Publisher / Repository:
- ACM
- Date Published:
- ISBN:
- 9798400703836
- Page Range / eLocation ID:
- 923 to 934
- Format(s):
- Medium: X
- Location:
- Vancouver BC Canada
- Sponsoring Org:
- National Science Foundation
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null (Ed.)Recently Cutler and Radcliffe proved that the graph on $n$ vertices with maximum degree at most $r$ having the most cliques is a disjoint union of $\lfloor n/(r+1)\rfloor$ cliques of size $r+1$ together with a clique on the remainder of the vertices. It is very natural also to consider this question when the limiting resource is edges rather than vertices. In this paper we prove that among graphs with $m$ edges and maximum degree at most $r$, the graph that has the most cliques of size at least two is the disjoint union of $\bigl\lfloor m \bigm/\binom{r+1}{2} \bigr\rfloor$ cliques of size $r+1$ together with the colex graph using the remainder of the edges.more » « less
