The CriticalSet problem: Identifying Critical Contributors in Bipartite Dependency Networks

Identifying critical nodes in complex networks is a fundamental task in graph mining. Yet, methods addressing an all-or-nothing coverage mechanics in a bipartite dependency network, a graph with two types of nodes where edges represent dependency relationships across the two groups only, remain largely unexplored. We formalize the CriticalSet problem: given an arbitrary bipartite graph modeling dependencies of items on contributors, identify the set of k contributors whose removal isolates the largest number of items. We prove that this problem is NP-hard and requires maximizing a supermodular set function, for which standard forward greedy algorithms provide no approximation guarantees. Consequently, we model CriticalSet as a coalitional game, deriving a closed-form centrality, ShapleyCov, based on the Shapley value. This measure can be interpreted as the expected number of items isolated by a contributor's departure. Leveraging these insights, we propose MinCov, a linear-time iterative peeling algorithm that explicitly accounts for connection redundancy, prioritizing contributors who uniquely support many items. Extensive experiments on synthetic and large-scale real datasets, including a Wikipedia graph with over 250 million edges, reveal that MinCov and ShapleyCov significantly outperform traditional baselines. Notably, MinCov achieves near-optimal performance, within 0.02 AUC of a Stochastic Hill Climbing metaheuristic, while remaining several orders of magnitude faster.

Project resilience as network robustness

Engineering projects are the result of the combined effort of their members. Yet, it has been documented that labor division withing projects is unevenly distributed: some project members are specialists undertaking only few tasks, whereas other are generalists and are responsible for the success of many tasks. Moreover, the latter are often facilitators of project integration. Such a workload distribution prompts one question: how resilient is a project to key personnel loss? Far from being a theoretical problem, the reliance of a project on a few key people can lead to severe economic losses and delays. We argue that current methods to estimate such a risk are unsatisfactory: some methods offer a best-case estimate and are, therefore, too optimistic; other methods fail to capture project fragmentation leading to biased estimates and unrealistic consequences in many settings. In this paper, we develop a novel method to assess project vulnerability by looking at it from the lens of network robustness. We compare our method against existing alternatives and show that it offers better and more consistent estimates of project resilience to personnel loss.