Breadth-first traversal of trees and integer sorting in parallel

Abstract

We present a cost-optimal parallel algorithm for traversing a general tree in breadth-first fashion. For a tree with n nodes, this algorithm requires O( n/ p+log n) time employing p processors on the EREW PRAM model. To the best of our knowledge, it is the first parallel algorithm for breadth-first tree-traversal, which has O(log n) time complexity and yet being cost-optimal for p=O( n/log n) on the EREW PRAM. Our approach is based on a novel idea which converts the breadth-first traversal problem into a parentheses matching problem. As an application of this technique, we design a simple but elegant parallel algorithm for sorting a special class of integers in which elements in any two consecutive places of the input sequence differ at most by unity. The proposed sorting algorithm is stable and it achieves the same performance as that of our breadth-first traversal algorithm.