Main-memory triangle computations for very large (sparse (power-law)) graphs

Finding, counting and/or listing triangles (three vertices with three edges) in massive graphs are natural fundamental problems, which have recently received much attention because of their importance in complex network analysis. Here we provide a detailed survey of proposed main-memory solutions to...

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Bibliographic Details
Published in:Theoretical computer science Vol. 407; no. 1; pp. 458 - 473
Main Author: Latapy, Matthieu
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 06.11.2008
Elsevier
Subjects:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Complex networks
Computer Science
Computer science; control theory; systems
Exact sciences and technology
Graphs
Information retrieval. Graph
Mathematical analysis
Mathematics
Miscellaneous
Sciences and techniques of general use
Several complex variables and analytic spaces
Theoretical computing
Triangles
Graphs
Algorithms
Triangles
Complex networks
Edge(graph)
Computer theory
Memory
Triangle
Experimental study
Algorithm
Space complexity
Survey
Network analysis
Network
Counting
Power
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:Finding, counting and/or listing triangles (three vertices with three edges) in massive graphs are natural fundamental problems, which have recently received much attention because of their importance in complex network analysis. Here we provide a detailed survey of proposed main-memory solutions to these problems, in a unified way. We note that previous authors have paid surprisingly little attention to space complexity of main-memory solutions, despite its both fundamental and practical interest. We therefore detail space complexities of known algorithms and discuss their implications. We also present new algorithms which are time optimal for triangle listing and beats previous algorithms concerning space needs. They have the additional advantage of performing better on power-law graphs, which we also detail. We finally show with an experimental study that these two algorithms perform very well in practice, allowing us to handle cases which were previously out of reach.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2008.07.017