Cost-optimal parallel algorithms for traversing trees

The authors present cost-optimal parallel algorithms for depth-order (e.g., pre-, in-, and post-order) and level-order (e.g., breadth-first and breadth-depth) traversals of general trees with n nodes. Each of the algorithms requires O(n/p+log n) time using p⩽n processors on the EREW (exclusive read, exclusive write) PRAM (parallel random access machine) model. The breadth-first and breadth-depth algorithms attain O(log n) time complexity and yet are cost-optimal for p⩽n/log n processors. The proposed approach to the three depth-order traversals uses only a single characterization of the generic problem. The breadth-first tree-traversal algorithm utilizes a novel idea which converts this problem into a parentheses matching problem, while the breadth-depth algorithm is obtained by reducing the problem into a variety of (general) linked list ranking problems