An O(log n) Parallel Algorithm for Constructing a Spanning Tree on Permutation Graphs

Let G = (V, E) be a graph with n vertices and m edges. The problem of constructing a spanning tree is to find a connected subgraph of G with n vertices and (n 1) edges. For a weighted graph, the minimum spanning tree problem can be solved in O(log m) time with O(m) processors on the CRCW PRAM, and for an unweighed graph, the spanning tree problem can be solved in O(log n) time with O(n +m) processors on the CRCW PRAM. In this paper, we shall propose an O(log n> time parallel algorithm with O(n/log n) processors on the EREW PRAM for constructing a spanning tree on an unweighted permutation graph.