buTCS: An Optimized Algorithm for Estimating the Size of Transitive Closure

Given a directed graph and a node
$v$
, the transitive closure (
TC
) of
$v$
is the set of nodes that
$v$
can reach in the graph.
TC
size is very important in many applications but the cost of
TC
size computation is high in both time and space, which makes computing accurate
TC
size not applicable to the scenario where we need to know the
TC
size quickly for large graphs. Considering that existing approaches are either inefficient or inaccurate, we propose an algorithm, namely
buTCS
, to efficiently make more accurate estimation. Our approach works in linear time and space. The basic idea is to compute a node’s
TC
size based on that of its out-neighbors and perform a top-down verification. We further propose two optimizations to improve the estimation accuracy. The experimental results on 13 real datasets show that
buTCS
achieves better estimation on
TC
size efficiently.