Seeding with Costly Network Information
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The spread of behavior over social networks depends on the contact structure among individuals, and seeding the most influential agents can substantially enhance the extent of the spread. While the choice of the best seed set, known as influence maximization, is a computationally hard problem, many computationally efficient algorithms have been proposed to approximate the optimal seed sets with provable guarantees. Most of the previous work on influence maximization assumes the knowledge of the entire network graph. However, in practice, obtaining full knowledge of the network structure is very costly. In this work, we consider the choice of k initial seeds to maximize the expected number of adopters under the independent cascade model. We propose a "probe-and-seed" algorithm that provides almost tight approximation guarantees using Õ(p n^2 + √(p) n^1.5) edge queries in Õ(p n^2 + √(p) n^1.5) time, where n is the network size and p is the probability of spreading through an edge. To the best of our knowledge, this is the first result to provide approximation guarantees for influence maximization, using a sub-quadratic number of queries for polynomially small p. We complement this result by showing that it is impossible to approximate the problem using o(n^2) edge queries for constant p. In the end, we consider a more advanced query model, where one seeds a node and observes the resultant adopters after running the spreading process. We provide an algorithm that uses only Õ(k^2) such queries and provides almost tight approximation guarantees.
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