Ranking and unranking trees with a given number or a given set of leaves
msra(2010)
摘要
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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关键词
complete graph,spanning tree
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