Given a social network represented by a graph G, we consider the problem of finding a bounded cardinality set of nodes S with the property that the influence spreading from S in G is as large as possible. The dynamics that govern the spread of influence is the following: initially only elements in S are in- fluenced; subsequently at each round, the set of influenced elements is augmented by all nodes in the network that have a sufficiently large number of already influ- enced neighbors. While it is known that the general problem is hard to solve — even in the approximate sense — we present exact polynomial time algorithms for trees, paths, cycles, and complete graphs.
How to go Viral: Cheaply and Quickly
Cicalese, Ferdinando;
2014-01-01
Abstract
Given a social network represented by a graph G, we consider the problem of finding a bounded cardinality set of nodes S with the property that the influence spreading from S in G is as large as possible. The dynamics that govern the spread of influence is the following: initially only elements in S are in- fluenced; subsequently at each round, the set of influenced elements is augmented by all nodes in the network that have a sufficiently large number of already influ- enced neighbors. While it is known that the general problem is hard to solve — even in the approximate sense — we present exact polynomial time algorithms for trees, paths, cycles, and complete graphs.
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