Searching Personalized $k$-wing in Large and Dynamic Bipartite Graphs

TL;DR

This paper introduces efficient index structures, EquiWing and EquiWing-Comp, for personalized $k$-wing search in large, dynamic bipartite graphs, enabling fast, query-dependent cohesive subgraph retrieval.

Contribution

It proposes novel index structures and algorithms for personalized $k$-wing search, along with maintenance strategies for evolving bipartite graphs, improving efficiency and scalability.

Findings

EquiWing and EquiWing-Comp significantly outperform baseline methods.

The proposed indices enable linear-time personalized $k$-wing search.

Maintenance algorithms effectively handle graph updates with low cost.

Abstract

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 the personalized $k$-wing search problem. We introduce a $k$-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. Further, we propose a more compact version of EquiWing, EquiWing-Comp, which is achieved by integrating 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, large-scale graphs to validate the efficiency and effectiveness of EquiWing and EquiWing-Comp compared to the baseline.