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PUBLICATIONS

Counting the Leaves of Trees

Published

Author(s)

Brian D. Cloteaux, Luis A. Valentin

Abstract

A number of important combinatorial counting problems can be reformulated into the problem of counting the number of leaf nodes on a tree. Since the basic leaf-counting problem is #P-complete, there is strong evidence that no polynomial time algorithm exists for this general problem. Thus, we propose a randomized approximation scheme for this problem, and then empirically compare its convergence rate with the classic method of Knuth. We then give an application of our scheme by introducing a new algorithm for estimating the number of bases of a matroid with an independence oracle.
Citation
Congressus Numerantium
Volume
207
Pub Type
Journals

Download Paper

Local Download

Keywords

randomized algorithm, combinatorial enumeration
Mathematics and statistics

Citation

Cloteaux, B. and Valentin, L. (2011), Counting the Leaves of Trees, Congressus Numerantium, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=908869 (Accessed October 8, 2025)

Issues

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Created December 19, 2011, Updated February 19, 2017
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