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2013 IEEE 13th International Conference on Data Mining (2013)
Dallas, TX, USA USA
Dec. 7, 2013 to Dec. 10, 2013
ISSN: 1550-4786
pp: 11-20
A fundamental problem in many applications involving social and biological networks is to identify and count the number of embeddings of a given small sub graph in a large graph. Often, they involve dynamic graphs, in which the graph changes incrementally (e.g., by edge addition/deletion). We study the Dynamic Sub graph Enumeration (DSE) Problem, where the goal is to maintain a dynamic data structure to solve the sub graph enumeration problem efficiently when the graph changes incrementally. We develop a new data structure that combines two techniques: (i) the color-coding technique of Alon et al., 2008, for enumerating trees, and (ii) a dynamic data structure for maintaining the h-index of the graph (developed by Eppstein and Spiro, 2009). We derive worst case bounds for the update time in terms of the h-index of the graph and the maximum degree. We also study the empirical performance of our algorithm in a large set of real networks, and find significant improvement over the static methods.
Data structures, Heuristic algorithms, Approximation algorithms, Approximation methods, Color, Algorithm design and analysis, Silicon

A. Adiga, A. K. Vullikanti and D. Wiggins, "Subgraph Enumeration in Dynamic Graphs," 2013 IEEE 13th International Conference on Data Mining(ICDM), Dallas, TX, USA USA, 2013, pp. 11-20.
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