I/O-Efficient Algorithms for Degeneracy Computation on Massive Networks

Degeneracy is an important concept to measure the sparsity of a graph which has been widely used in many network analysis applications. Many network analysis algorithms, such as clique enumeration and truss decomposition, perform very well in graphs having small degeneracies. In this paper, we propo...

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Bibliographic Details
Published in:IEEE transactions on knowledge and data engineering Vol. 34; no. 7; pp. 3335 - 3348
Main Authors: Li, Rong-Hua, Song, Qiushuo, Xiao, Xiaokui, Qin, Lu, Wang, Guoren, Yu, Jeffrey Xu, Mao, Rui
Format: Journal Article
Language:English
Published: New York IEEE 01.07.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
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Algorithms
Clustering algorithms
Complexity theory
Degeneracy
Electronic mail
Enumeration
Graph theory
Graphs
Heuristic algorithms
I/O-efficient algorithm
massive graphs
Memory management
Network analysis
Nodes
Prediction algorithms
Social network services
ISSN:1041-4347, 1558-2191
Online Access:Get full text
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Summary:Degeneracy is an important concept to measure the sparsity of a graph which has been widely used in many network analysis applications. Many network analysis algorithms, such as clique enumeration and truss decomposition, perform very well in graphs having small degeneracies. In this paper, we propose an I/O-efficient algorithm to compute the degeneracy of the massive graph that cannot be fully kept in the main memory. The proposed algorithm only uses <inline-formula><tex-math notation="LaTeX">O(n)</tex-math> <mml:math><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="wang-ieq1-3021484.gif"/> </inline-formula> memory, where <inline-formula><tex-math notation="LaTeX">n</tex-math> <mml:math><mml:mi>n</mml:mi></mml:math><inline-graphic xlink:href="wang-ieq2-3021484.gif"/> </inline-formula> denotes the number of nodes of the graph. We also develop an I/O-efficient algorithm to incrementally maintain the degeneracy on dynamic graphs. Extensive experiments show that our algorithms significantly outperform the state-of-the-art degeneracy computation algorithms in terms of both running time and I/O costs. The results also demonstrate high scalability of the proposed algorithms. For example, in a real-world web graph with 930 million nodes and 13.3 billion edges, the proposed algorithm takes only 633 seconds and uses less than 4.5GB memory to compute the degeneracy.
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ISSN:1041-4347
1558-2191
DOI:10.1109/TKDE.2020.3021484