Worst-Case Scenarios for Greedy, Centrality-Based Network Protection Strategies

The task of allocating preventative resources to a computer network in order to protect against the spread of viruses is addressed. Virus spreading dynamics are described by a linearized SIS model and protection is framed by an optimization problem which maximizes the rate at which a virus in the network is contained given finite resources. One approach to problems of this type involve greedy heuristics which allocate all resources to the nodes with large centrality measures. We address the worst case performance of such greedy algorithms be constructing networks for which these greedy allocations are arbitrarily inefficient. An example application is presented in which such a worst case network might arise naturally and our results are verified numerically by leveraging recent results which allow the exact optimal solution to be computed via geometric programming.

💡 Research Summary

The paper addresses the problem of allocating limited preventive resources (e.g., patches, firewalls, or vaccination analogues) across a computer network in order to curb the spread of malicious software. The authors model virus propagation with a linearized susceptible‑infected‑susceptible (SIS) process, specifically the heterogeneous N‑intertwined SIS (HeNiSIS) model, where each node i has its own infection rate β_i and a common recovery rate δ. Under a mean‑field approximation the dynamics are governed by the matrix B W − δI, where B=diag(β) and W is the weighted adjacency matrix. The disease‑free equilibrium is exponentially stable if the largest real part of the eigenvalues of B W − δI is less than –ε for some ε>0.

The resource‑allocation problem (Problem 1) is to choose β_i within a feasible interval