  In this paper we provide a parallel algorithm that given any $n$-node
$m$-edge directed graph and source vertex $s$ computes all vertices reachable
from $s$ with $\tilde{O}(m)$ work and $n^{1/2 + o(1)}$ depth with high
probability in $n$ . This algorithm also computes a set of $\tilde{O}(n)$ edges
which when added to the graph preserves reachability and ensures that the
diameter of the resulting graph is at most $n^{1/2 + o(1)}$. Our result
improves upon the previous best known almost linear work reachability algorithm
due to Fineman which had depth $\tilde{O}(n^{2/3})$.
  Further, we show how to leverage this algorithm to achieve improved
distributed algorithms for single source reachability in the CONGEST model. In
particular, we provide a distributed algorithm that given a $n$-node digraph of
undirected hop-diameter $D$ solves the single source reachability problem with
$\tilde{O}(n^{1/2} + n^{1/3 + o(1)} D^{2/3})$ rounds of the communication in
the CONGEST model with high probability in $n$. Our algorithm is nearly optimal
whenever $D = O(n^{1/4 - \epsilon})$ for any constant $\epsilon > 0$ and is the
first nearly optimal algorithm for general graphs whose diameter is
$\Omega(n^\delta)$ for any constant $\delta$.
