Budget-constrained Truss Maximization over Large Graphs: A Component-based Approach

Abstract

Cohesive substructure identification is one fundamental task of graph analytics. Recently, a useful problem of dense subgraph maximization has attracted significant attentions, which aims at enlarging a dense subgraph pattern using a few new edge insertions, e.g., k-core maximization. As a more cohesive subgraph of k-core, k-truss requires that each edge has at least k-2 triangles within this subgraph. However, the problem of k-truss maximization has not been studied yet. In this paper, we motivate and formulate a new problem of budget-constrained k-truss maximization. Given a budget of b edges and an integer k≥2, the problem is to find and insert b new edges into a graph G such that the resulted k-truss of G is maximized. We theoretically prove the NP-hardness of k-truss maximization problem. To efficiently tackle it, we analyze non-submodular property of k-truss newcomers function and develop non-conventional heuristic strategies for edge insertions. We first identify high-quality candidate edges with regard to (k-1)-light subgraphs and propose a greedy algorithm using per-edge insertion. Besides further improving the efficiency by pruning disqualified candidate edges, we finally develop a component-based dynamic programming algorithm for enlarging k-truss mostly, which makes a balance of budget assignment and inserts multiple edges simultaneously into all (k-1)-light components. Extensive experiments on nine real-world graphs demonstrate the efficiency and effectiveness of our proposed methods.