  Measuring and optimizing the influence of nodes in big-data online social
networks are important for many practical applications, such as the viral
marketing and the adoption of new products. As the viral spreading on social
network is a global process, it is commonly believed that measuring the
influence of nodes inevitably requires the knowledge of the entire network.
Employing percolation theory, we show that the spreading process displays a
nucleation behavior: once a piece of information spread from the seeds to more
than a small characteristic number of nodes, it reaches a point of no return
and will quickly reach the percolation cluster, regardless of the entire
network structure, otherwise the spreading will be contained locally. Thus, we
find that, without the knowledge of entire network, any nodes' global influence
can be accurately measured using this characteristic number, which is
independent of the network size. This motivates an efficient algorithm with
constant time complexity on the long standing problem of best seed spreaders
selection, with performance remarkably close to the true optimum.
