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The problem of identifying important players in a given network is of pivotalimportance for viral marketing, public health management, network security andvarious other fields of social network analysis. In this work we find the mostimportant vertices in a graph G = (V,E) to immunize so as the chances of anepidemic outbreak is minimized. This problem is directly relevant to minimizingthe impact of a contagion spread (e.g. flu virus, computer virus and rumor) ina graph (e.g. social network, computer network) with a limited budget (e.g. thenumber of available vaccines, antivirus software, filters). It is well knownthat this problem is computationally intractable (it is NP-hard). In this workwe reformulate the problem as a budgeted combinational optimization problem anduse techniques from spectral graph theory to design an efficient greedyalgorithm to find a subset of vertices to be immunized. We show that ouralgorithm takes less time compared to the state of the art algorithm. Thus ouralgorithm is scalable to networks of much larger sizes than best knownsolutions proposed earlier. We also give analytical bounds on the quality ofour algorithm. Furthermore, we evaluate the efficacy of our algorithm on anumber of real world networks and demonstrate that the empirical performance ofalgorithm supplements the theoretical bounds we present, both in terms ofapproximation guarantees and computational efficiency.

Scalable Approximation Algorithm for Network Immunization