Searching Personalized k-Wing in Bipartite Graphs

There are extensive studies focusing on the application scenario that all the bipartite cohesive subgraphs need to be discovered in a bipartite graph. However, we observe that, for some applications, one is interested in finding bipartite cohesive subgraphs containing a specific vertex. In this paper, we study a new query-dependent bipartite cohesive subgraph search problem based on k-wing model, named as personalized k-wing search problem. We study the k-wing equivalence relationship to summarize the edges of a bipartite graph G into groups. Therefore, all the edges of G are segregated into different groups, i.e., k-wing equivalence class, forming an efficient and wing number conserving index called EquiWing-Graph. Further, we propose a more compact index, EquiWing-Tree, which is achieved by using our proposed k-butterfly loose approach and discovered hierarchy properties. These indices are used to expedite the personalized k-wing search with a non-repetitive access to G, which leads to linear algorithms for searching the personalized k-wing. Moreover, we conduct a thorough study on the maintenance of the proposed indices for evolving bipartite graphs. We discover novel properties that help us localize the scope of the maintenance at a low cost. By exploiting the discoveries, we propose novel algorithms for maintaining the two indices, which substantially reduces the cost of maintenance. We perform extensive experimental studies in real-world graphs to validate the efficiency and effectiveness of EquiWing-Graph and EquiWing-Tree compared to the baseline.