Abstract
Alice wants to join a new social network, and influence its members to adopt a new product or idea. Each person v in the network has a certain threshold t(v) for activation, i.e. adoption of the product or idea. If v has at least t(v) activated neighbors, then v will also become activated. If Alice wants to make k new friends in the network, and thereby activate the most number of people, how should she choose these friends? We study the problem of choosing the k people in the network to befriend, who will in turn activate the maximum number of people. This Maximum Influence with Links Problem has applications in viral marketing and the study of epidemics. We show that the solution can be quite different from the related and widely studied influence maximization problem where the objective is to choose a seed or target set with maximum influence. We prove that the Maximum Influence with Links problem is NP-complete even for bipartite graphs in which all nodes have threshold 1 or 2. In contrast, we give polynomial time algorithms that find optimal solutions for the problem for trees, paths, cycles, and cliques.
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