Cover Edge-Based Novel Triangle Counting
arxiv(2024)
摘要
Listing and counting triangles in graphs is a key algorithmic kernel for
network analyses, including community detection, clustering coefficients,
k-trusses, and triangle centrality. In this paper, we propose the novel concept
of a cover-edge set that can be used to find triangles more efficiently.
Leveraging the breadth-first search (BFS) method, we can quickly generate a
compact cover-edge set. Novel sequential and parallel triangle counting
algorithms that employ cover-edge sets are presented. The novel sequential
algorithm performs competitively with the fastest previous approaches on both
real and synthetic graphs, such as those from the Graph500 Benchmark and the
MIT/Amazon/IEEE Graph Challenge. We implement 22 sequential algorithms for
performance evaluation and comparison. At the same time, we employ OpenMP to
parallelize 11 sequential algorithms, presenting an in-depth analysis of their
parallel performance. Furthermore, we develop a distributed parallel algorithm
that can asymptotically reduce communication on massive graphs. In our estimate
from massive-scale Graph500 graphs, our distributed parallel algorithm can
reduce the communication on a scale 36 graph by 1156x and on a scale 42 graph
by 2368x. Comprehensive experiments are conducted on the recently launched
Intel Xeon 8480+ processor and shed light on how graph attributes, such as
topology, diameter, and degree distribution, can affect the performance of
these algorithms.
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