IEEE Transactions on Parallel and Distributed Systems

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Keywords

Cayleys Tree Formula, Dominance Counting Problem, Labeled Trees, Parallel Algorithms, Prufer Mapping

Abstract

Abstract—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. 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 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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