  For a connected graph, a vertex separator is a set of vertices whose removal
creates at least two components and a minimum vertex separator is a vertex
separator of least cardinality. The vertex connectivity refers to the size of a
minimum vertex separator. For a connected graph $G$ with vertex connectivity $k
(k \geq 1)$, the connectivity augmentation refers to a set $S$ of edges whose
augmentation to $G$ increases its vertex connectivity by one. A minimum
connectivity augmentation of $G$ is the one in which $S$ is minimum. In this
paper, we focus our attention on connectivity augmentation of trees. Towards
this end, we present a new sequential algorithm for biconnectivity augmentation
in trees by simplifying the algorithm reported in \cite{nsn}. The simplicity is
achieved with the help of edge contraction tool. This tool helps us in getting
a recursive subproblem preserving all connectivity information. Subsequently,
we present a parallel algorithm to obtain a minimum connectivity augmentation
set in trees. Our parallel algorithm essentially follows the overall structure
of sequential algorithm. Our implementation is based on CREW PRAM model with
$O(\Delta)$ processors, where $\Delta$ refers to the maximum degree of a tree.
We also show that our parallel algorithm is optimal whose processor-time
product is O(n) where $n$ is the number of vertices of a tree, which is an
improvement over the parallel algorithm reported in \cite{hsu}.
