Fabrizio Altarelli, Alfredo Braunstein, Luca Dall'Asta, Riccardo Zecchina
We analyze the irreversible dynamical process corresponding to the linear-threshold model of influence spread over a network, and propose an efficient algorithm to solve the inverse problem, namely that of finding an optimal initial condition that generates to a desired final state of the dynamics. This is a challenging problem which is crucial in many contexts, from systemic risk analysis to the design of viral marketing campaigns. Our approach is based on the cavity-method of statistical physics. We compare our algorithm to standard techniques (based on Monte Carlo and Linear Programming) and show that it has an excellent performance.
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http://arxiv.org/abs/1203.1426
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