Ranking and unranking trees with a given number or a given set of leaves
Combinatorics
2010-09-13 v1
Abstract
In this paper, we provide algorithms to rank and unrank certain degree-restricted classes of Cayley trees (spanning trees of the n-vertex complete graph). Specifically, we consider classes of trees that have a given set of leaves or a fixed number k of leaves. For fixed k, the number of Cayley trees with n vertices and k leaves grows roughly as n! and hence the ranks have O(nlog_2(n)) bits. Our ranking and unranking algorithms require at most O(n^2) comparisons of numbers less than or equal to n plus O(n) operations of multiplication, division, addition, substraction and comparision on numbers of length O(nlog(n)).
Keywords
Cite
@article{arxiv.1009.2060,
title = {Ranking and unranking trees with a given number or a given set of leaves},
author = {Jeffrey B. Remmel and S. Gill Williamson},
journal= {arXiv preprint arXiv:1009.2060},
year = {2010}
}