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A parallel algorithm for constructing a labeled tree

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3 Author(s)
Yue-Li Wang ; Dept. of Ind. Manage., Nat. Taiwan Inst. of Technol., Taipei, Taiwan ; Hon-Chan Chen ; Wei-Kai Liu

A tree T is labeled when the n vertices are distinguished from one another by names such as v1, v2…vn . Two labeled trees are considered to be distinct if they have different vertex labels even though they might be isomorphic. According to Cayley's tree formula, there are nn-2 labeled trees on n vertices. Prufer used a simple way to prove this formula and demonstrated that there exists a mapping between a labeled tree and a number sequence. From his proof, we can find a naive sequential algorithm which transfers a labeled tree to a number sequence and vice versa. However, it is hard to parallelize. In this paper, we shall propose an O(log n) time parallel algorithm for constructing a labeled tree by using O(n) processors and O(n log n) space on the EREW PRAM computational model

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Parallel and Distributed Systems, IEEE Transactions on  (Volume:8 ,  Issue: 12 )