Fast Parallel Algorithm for Finding the kth Longest Path in A Tree

We present a fast parallel algorithm running in O(log 2 n) time on a CREW PRAM with O(n) processors for nding the kth longest path in a given tree of n vertices (with (n 2) intervertex distances). Our algorithm is obtained by e cient parallelization of a sequential algorithm which isavariant of both Megiddo et al's algorithm [12] andFredrickson et al's algorithm [3] 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. Keywords: Centroid of a tree, decomposition, kth longest path, parallel algorithm, PRAM, selection in ordered matrices