  The vital nodes are the ones that play an important role in the organization
of network structure or the dynamical behaviours of networked systems. Previous
studies usually applied the node centralities to quantify the importance of
nodes. Realizing that the percolation clusters are dominated by local
connections in the subcritical phase and by global connections in the
supercritical phase, in this paper we propose a new method to identify the
vital nodes via a competitive percolation process that is based on an
Achlioptas process. Compared with the existing node centrality indices, the new
method performs overall better in identifying the vital nodes that maintain
network connectivity and facilitate network synchronization when considering
different network structure characteristics, such as link density, degree
distribution, assortativity, and clustering. We also find that our method is
more tolerant of noisy data and missing data. More importantly, compared with
the unique ranking list of nodes given by most centrality methods, the
randomness of the percolation process expands the possibility space of the
optimal solutions, which is of great significance in practical applications.
