Accelerating community-search problem through faster graph dedensification

Community-search is the problem of finding a densely connected subgraph from a large graph, for given set of query nodes. It is useful, for example, when some high profiled researchers want to arrange a conference or some celebrities wish to arrange a party, and are searching for other researchers and similar personalties respectively. Technically, the problem involves maximizing the minimum degree to find a highly connected subgraph. Well known Greedy algorithm for this purpose, iteratively deletes nodes with minimum degree to meet certain objective function. We observe that Greedy operates in an in-efficient manner due to densely connected regions in a graph, referred as Hot Spots. In this paper, we provide a new concept of performing community-search on a dedensified graph. Our aim is to sparsify the hot spots to accelerate global searching method of Greedy to make it applicable on a large graph. Recently a graph dedensification approach has been proposed that adds Compressor Nodes in a graph for dedensification. However, this method is in-efficient since it has to traverse entire graph to compress the hot spots. To solve this problem, we propose a faster graph dedensification algorithm by using Locality Sensitive Hashing (LSH). We improve time complexity of existing graph dedensification method from O (|E|) to O (|N|+|eHDN|+k), where N, E, eHDN, and k are nodes, edges, edges of High Degree Nodes (HDN), and hash functions respectively, and |N| ≫ |HDN|. Once the graph is dedensified, we use it to accelerate community-search operation. We perform experiments on two real world graphs, and observe significant improvement in execution time of Greedy algorithm, add lesser compressor nodes, and perform reduced traversals for graph dedensification.