Maximal size constraint community search over bipartite graphs

Community search over bipartite graphs is a crucial issue with significant applications in various domains, including group recommendations, fraud detection and representation learning. Current research primarily focuses on the structural cohesiveness constraint between two sets of vertices, often neglecting the community’s size constraint. Unfortunately, this oversight may lead to communities of sizes ranging from excessively small to substantially large, thereby affecting their applicability. Therefore, in this paper, we focus on the maximal size constraint community search over bipartite graphs, which not only takes into account the (α,β) degree constraints for each set of vertices but also ensures that the number of vertices in each set is limited to ξ and ζ, respectively. To solve this problem, we first introduce two competitive algorithms, namely Ordering-based Expansion Algorithm (OEA) and Followers-based Peeling Algorithm (FPA), wherein they greedily expand or peel vertices, respectively, to identify the maximal one in a breadth-first manner, utilizing a novel vertex ordering and followers concept. To further accelerate the computation, we propose an advanced Expand-and-Filter Algorithm (EFA++) that first acquires a slightly larger community and subsequently executes a filtering phase employing a dynamic programming technique. Furthermore, we define the “Affected Area” for edge insertion or deletion that caters for dynamic scenarios. Finally, the theoretical analysis and extensive experimental evaluation on several real-life datasets demonstrate the effectiveness and efficiency of the proposed algorithms.