An Efficient Approach to Finding Dense Temporal Subgraphs

• Published in: IEEE transactions on knowledge and data engineering Vol. 32; no. 4; pp. 645 - 658
• Main Authors: Ma, Shuai, Hu, Renjun, Wang, Luoshu, Lin, Xuelian, Huai, Jinpeng
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Aggregates; Algorithms; Approximation algorithms; big data; Dense subgraphs; evolving convergence; Graph theory; Heuristic algorithms; Networks; Roads; Semantics; statistics driven approaches; Steiner trees; temporal networks; Urban areas
• ISSN: 1041-4347; 1558-2191
• DOI: 10.1109/TKDE.2019.2891604

Dense subgraph discovery has proven useful in various applications of temporal networks. We focus on a special class of temporal networks whose nodes and edges are kept fixed, but edge weights regularly vary with timestamps. However, finding dense subgraphs in temporal networks is non-trivial, and its state of the art solution uses a filter-and-verification framework that is not scalable on large temporal networks. In this study, we propose a highly efficient approach to finding dense subgraphs in large temporal networks with <inline-formula><tex-math notation="LaTeX">T</tex-math> <mml:math><mml:mi>T</mml:mi></mml:math><inline-graphic xlink:href="ma-ieq1-2891604.gif"/> </inline-formula> timestamps. (1) We first develop a statistics-driven approach that employs hidden statistics to identifying <inline-formula><tex-math notation="LaTeX">k</tex-math> <mml:math><mml:mi>k</mml:mi></mml:math><inline-graphic xlink:href="ma-ieq2-2891604.gif"/> </inline-formula> time intervals, instead of <inline-formula><tex-math notation="LaTeX">T(T+1)/2</tex-math> <mml:math><mml:mrow><mml:mi>T</mml:mi><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href="ma-ieq3-2891604.gif"/> </inline-formula> ones (<inline-formula><tex-math notation="LaTeX">k</tex-math> <mml:math><mml:mi>k</mml:mi></mml:math><inline-graphic xlink:href="ma-ieq4-2891604.gif"/> </inline-formula> is typically much smaller than <inline-formula><tex-math notation="LaTeX">T</tex-math> <mml:math><mml:mi>T</mml:mi></mml:math><inline-graphic xlink:href="ma-ieq5-2891604.gif"/> </inline-formula>), which strikes a balance between quality and efficiency. (2) After proving that the problem has no constant factor approximation algorithms, we design better heuristic algorithms to attack the problem, by connecting finding dense subgraphs with a variant of the Prize Collecting Steiner Tree problem. (3) Finally, we have conducted an extensive experimental study to verify that our approach is both effective and efficient.