Abstract
Bipartite networks, which model relationships between two different types of entities, are prevalent in many real-world applications. On bipartite networks, the cascading node departure undermines the networks' ability to provide sustainable services, which makes reinforcing bipartite networks a vital problem. Although network reinforcement is extensively studied on unipartite networks, it remains largely unexplored on bipartite graphs. On bipartite networks, (<tex>$\alpha, \beta$</tex>) -core is a stable structure that ensures different minimum engagement levels of the vertices from different layers, and we aim to reinforce bipartite networks by maximizing the (<tex>$\alpha, \beta$</tex>) -core. Specifically, given a bipartite network <tex>$G$</tex>, degree constraints <tex>$\alpha$</tex> and <tex>$\beta$</tex>, budgets <tex>$b_{1}$</tex> and <tex>$b_{2}$</tex>, we aim to find <tex>$b_{1}$</tex> upper layer vertices and <tex>$b_{2}$</tex> lower layer vertices as anchors and bring them into the (<tex>$\alpha, \beta$</tex>) -core s.t. the number of non-anchor vertices entering in the (<tex>$\alpha, \beta$</tex>) -core is maximized. We prove the problem is NP-hard and propose a heuristic algorithm FILVER to solve the problem. FILVER runs <tex>$b_{1}+b_{2}$</tex> iterations and choose the best anchor in each iteration. Under a filter-verification framework, it reduces the pool of candidate anchors (in the filter stage) and computes the resulting (<tex>$\alpha, \beta$</tex>) - core for each anchor vertex more efficiently (in the verification stage). In addition, filter-stage optimizations are proposed to further reduce “dominated” anchors and allow computation-sharing across iterations. To optimize the verification stage, we explore the cumulative effect of placing multiple anchors, which effectively reduces the number of running iterations. Extensive experiments on 18 real-world datasets and a billion-scale synthetic dataset validate the effectiveness and efficiency of our proposed techniques.
Published Version
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