Influence Diffusion in Social Networks under Time Window Constraints

Abstract

We study a combinatorial model of the spread of influence in networks that generalizes existing schemata recently proposed in the literature. In our model, agents change behaviors/opinions on the basis of information collected from their neighbors in a time interval of bounded size whereas agents are assumed to have unbounded memory in previously studied scenarios. In our mathematical framework, one is given a network G = (V, E), an integer value t(v) for each node v ∈ V , and a time window size λ. The goal is to determine a small set of nodes (target set) that influences the whole graph. The spread of influence proceeds in rounds as follows: initially all nodes in the target set are influenced; subsequently, in each round, any uninfluenced node v becomes influenced if the number of its neighbors that have been influenced in the previous λ rounds is greater than or equal to t(v). We prove that the problem of finding a minimum cardinality target set that influences the whole network G is hard to approximate within a polylogarithmic factor. On the positive side, we design exact polynomial time algorithms for paths, rings, trees, and complete graphs.

Um estudo computacional do Problema do Gnosticismo Perfeito

“…Em trabalhos futuros, pretendemos investigar variações do PAP tais como o exemplo supracitado além de problemas relacionados como o PESP e o MESP (veja Seção 3.4). Visamos também estudar uma versão do TSSP, proposta em [28], na qual assume-se que um disseminador propaga a informação somente durante um intervalo restrito de rodadas consecutivas. Nesse caso, a modelagem de como a propagação ocorre possui semelhanças com o processo de contágio epidemiológico de patógenos.…”