Triangle Counting Through Cover-Edges

TL;DR

This paper introduces a novel cover-edge set concept and algorithms for efficient triangle counting in large graphs, significantly reducing communication costs in parallel processing.

Contribution

It proposes a new cover-edge set approach and develops both sequential and parallel algorithms that improve efficiency and communication performance in triangle counting.

Findings

Parallel algorithm reduces communication by over 1000x on large graphs.

Sequential algorithm avoids unnecessary triangle checks.

Effective in real social network and synthetic graphs.

Abstract

Counting and finding triangles in graphs is often used in real-world analytics to characterize cohesiveness and identify communities in graphs. In this paper, we propose the novel concept of a cover-edge set that can be used to find triangles more efficiently. We use a breadth-first search (BFS) to quickly generate a compact cover-edge set. Novel sequential and parallel triangle counting algorithms are presented that employ cover-edge sets. The sequential algorithm avoids unnecessary triangle-checking operations, and the parallel algorithm is communication-efficient. The parallel algorithm can asymptotically reduce communication on massive graphs such as from real social networks and synthetic graphs from the Graph500 Benchmark. In our estimate from massive-scale Graph500 graphs, our new parallel algorithm can reduce the communication on a scale 36 graph by 1156x and on a scale 42 graph by 2368x.