  In many applications, it is necessary to retrieve pairs of vertices with the
path between them satisfying certain constraints, since regular expression is a
powerful tool to describe patterns of a sequence. To meet such requirements, in
this paper, we define regular expression (RE) query on graphs to use regular
expression to represent the constraints between vertices. To process RE queries
on large graphs such as social networks, we propose the RE query processing
method with the index size sublinear to the graph size. Considering that large
graphs may be randomly distributed in multiple machines, the parallel RE
processing algorithms are presented without the assumption of graph
distribution. To achieve high efficiency for complex RE query processing, we
develop cost-based query optimization strategies with only a small size
statistical information which is suitable for querying large graphs.
Comprehensive experimental results show that this approach works scale well for
large graphs.
