Ranking and unranking trees with a given number or a given set of leaves

Details Ranking and unranking trees with a given number or a given set of leaves Ranking and unranking trees with a given number or a given set of leaves

2010-09-10

arxiv.org/abs/1009.2060v1

Mathematics

Combinatorics

Scientific paper

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)).

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