An O(log n) parallel algorithm for constructing a spanning tree on permutation graphs

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Abstract

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(nlog n) processors on the EREW PRAM for constructing a spanning tree on an unweighted permutation graph.

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This work was supported by the National Science Council, Republic of China, under contract NSC-84-2213-E-011-008.

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