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 G 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. © 1995.
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