Coreness Maximization through Budget-Limited Edge Insertion

The Budget Limited Coreness Maximization (BLCM) problem aims to enhance average user engagement by activating a limited number of connections, i.e., inserting up to b edges to maximize the coreness gain of all vertices in a graph. Due to the cascading feature, we prove the BLCM is NP-hard, APX-hard, and not submodular, meaning greedy sequential edge insertion fails to deliver satisfactory results. As a result, solving BLCM requires combinatorial edge insertion and must face the combinatorial exploration difficulty. This paper proposes the first effective and polynomial-time approach to BLCM. It embeds local combinatorial optimization into global greedy search to boost the benefits of combinatorial optimization while restricting its complexity. Specifically, we propose efficient methods to evaluate the cascaded coreness improvements of two local combinatorial strategies, i.e., when a leader or a group of nodes increase their coreness values via local edge insertion. Note that the key difficulty lies in evaluating the cascading effects. Based on these, we propose three efficient combinatorial edge insertion strategies: (1) Leader-Centric Greedy Insertion (LCGI), (2) Group-Centric Greedy Insertion (GCGI), and (3) a Leader-Group Balance (LGB) insertion. LCGI greedily finds the most influential leader that can produce the highest coreness gain together with its followers. GCGI finds the most influential group that can promote the most coreness gain. LGB combines the two strategies to select edge combinations adaptively. We prove the low complexity of LCGI, GCGI and LGB. Experiments conducted on 13 real-world datasets highlight their practical utility and superiority over existing approaches.