On the Power of Planned Infections in Networks

Abstract

Over the last decade we have witnessed the rapid proliferation of online networks and Internet activity. Although such activity is generally considered a blessing, it also brings with it a large increase in risk of computer malware—malignant software that actively spreads from one computer to another. To date, the majority of existing models of malware spread use stochastic behavior, when the set of neighbors infected from the current set of infected nodes is chosen obliviously. In this work, we initiate the study of planned-infection strategies that can decide intelligently which neighbors of infected nodes to infect next in order to maximize their spread, while maintaining a “signature” similar to the oblivious stochastic infection strategy in order not to be discovered. We first establish that computing optimal and near-optimal planned strategies is computationally hard. We then identify necessary and sufficient conditions in terms of network structure and edge infection probabilities such that the planned process can infect polynomially more nodes than the stochastic process while maintaining a similar “signature” as the oblivious stochastic infection strategy. Among our results is a surprising connection between an additional structural quantity of interest in a network, the network toughness, and planned infections. Based on the network toughness, we characterize networks where existence of planned strategies that are pandemic (infect all nodes) is guaranteed, as well as efficiently computable.