Exploiting Efficient Densest Subgraph Discovering Methods for Big Data

Discovering the densest subgraph is important in graph analysis, which has wide-ranging applications from social network community mining to the discovery of biological network modules. However, the previous algorithms neglect the connectivity of the dense subgraph since it is a challenge to give consideration to both subgraph structure and time efficiency. As a result, it may lead to isolated subgraphs in the output though they aim to find one connected dense subgraph. Also, there are lack of efficient algorithms for big natural graphs, especially considering datasets become increasingly larger in this era of Big Data. Furthermore, previous algorithms fail to take advantage of various features of natural graphs (e.g., power-law degree distribution, homophyly of vertices, and power-law community size) which can be applied to improve the efficiency and precision of the densest subgraph discovery. To handle these problems, in this paper, we study the densest subgraph problem by designing two different algorithms based on different features that natural graphs have. First, by analyzing the features of natural graphs, we design a heuristic algorithm for discovering the connected densest subgraph for massive undirected graphs in a MapReduce framework by taking advantage of the features of natural graphs. Second, we propose an exact algorithm for big data for the problem of discovering the densest subgraph. Experimental results show that our algorithms are more time-efficient and precise than other algorithms.