Fast parallel algorithm for finding the kth longest path in a tree

We present a fast parallel algorithm running in O(log²n) time on a CREW PRAM with O(n) processors for finding the kth longest path in a given tree of n vertices (with Θ(n² ) intervertex distances). Our algorithm is obtained by efficient parallelization of a sequential algorithm which is a variant of both N. Megiddo et al.´s algorithm and G.N. Fredrickson et al.´s algorithm based on centroid decomposition of tree and succinct representation of the set of intervertex distances. With the same time and space bound as the best known result, our sequential algorithm maintains a shorter length of the decomposition tree