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<p><b>Abstract</b>—A tree <it>T</it> is labeled when the <it>n</it> vertices are distinguished from one another by names such as <tmath>$v_1, v_2 \cdots, v_n.$</tmath> 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 <it>n</it><super><it>n</it>−2</super> labeled trees on <it>n</it> vertices. Prüfer 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 <it>O</it>(log <it>n</it>) time parallel algorithm for constructing a labeled tree by using <it>O</it>(<it>n</it>) processors and <it>O</it>(<it>n</it> log <it>n</it>) space on the EREW PRAM computational model.</p>
Cayley's tree formula, dominance counting problem, labeled trees, parallel algorithms, Prüfer mapping.
Hon-Chan Chen, Wei-Kai Liu, Yue-Li Wang, "A Parallel Algorithm for Constructing a Labeled Tree", IEEE Transactions on Parallel & Distributed Systems, vol. 8, no. , pp. 1236-1240, December 1997, doi:10.1109/71.640015
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