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An Efficient Algorithm for Generating Prüfer Codes from Labelled Trees

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Abstract.

According to Cayley's tree formula, there are n n-2 labelled trees on n vertices. Prüfer gave a bijection between the set of labelled trees on n vertices and sequences of n-2 numbers, each in the range 1, 2, ..., n . Such a number sequence is called a Prüfer code. The straightforward implementation of his bijection takes O(n log n ) time. In this paper we propose an O(n) time algorithm for the same problem. Our algorithm can be easily parallelized so that a Prüfer code can be generated in O (log n ) time using O(n) processors on the EREW PRAM computational model.

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Authors and Affiliations

  1. Department of Information Management, National Taiwan University of Science and Technology, Taipei, Taiwan, Republic of China ylwang@cs.ntust.edu.tw, , , , , , TW

    H. -C. Chen & Y. -L. Wang

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  1. H. -C. Chen
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  2. Y. -L. Wang
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Received October 2, 1998, and in final form March 1, 1999.

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-C. Chen, H., -L. Wang, Y. An Efficient Algorithm for Generating Prüfer Codes from Labelled Trees. Theory Comput. Systems 33, 97–105 (2000). https://doi.org/10.1007/s002249910006

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  • DOI: https://doi.org/10.1007/s002249910006

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