In this paper, first given a directed network G and a vertex r \in V(G) , we propose a new exact algorithm to compute betweenness score of r. Our algorithm pre-computes a set {RF}(r), which is used to prune a huge amount of computations that do not contribute in the betweenness score of r. Then, for the cases where {RF}(r) is large, we present a randomized algorithm that samples from {RF}(r) and performs computations for only the sampled elements. We show that this algorithm provides (\epsilon ,\delta ) an -approximation of the betweenness score of r. Finally, we empirically evaluate our algorithms and show that they significantly outperform the most efficient existing algorithms, in terms of both running time and accuracy. Our experiments also show that our proposed algorithms can effectively compute betweenness scores of all vertices in a set of vertices.