  Given a network represented by a graph $G=(V,E)$, we consider a dynamical
process of influence diffusion in $G$ that evolves as follows: Initially only
the nodes of a given $S\subseteq V$ are influenced; subsequently, at each
round, the set of influenced nodes is augmented by all the nodes in the network
that have a sufficiently large number of already influenced neighbors. The
question is to determine a small subset of nodes $S$ (\emph{a target set}) that
can influence the whole network. This is a widely studied problem that
abstracts many phenomena in the social, economic, biological, and physical
sciences. It is known that the above optimization problem is hard to
approximate within a factor of $2^{\log^{1-\epsilon}|V|}$, for any $\epsilon
>0$. In this paper, we present a fast and surprisingly simple algorithm that
exhibits the following features: 1) when applied to trees, cycles, or complete
graphs, it always produces an optimal solution (i.e, a minimum size target
set); 2) when applied to arbitrary networks, it always produces a solution of
cardinality which improves on the previously known upper bound; 3) when applied
to real-life networks, it always produces solutions that substantially
outperform the ones obtained by previously published algorithms (for which no
proof of optimality or performance guarantee is known in any class of graphs).

Data Structures and Algorithms;Social and Information Networks;Combinatorics;Physics and Society