Binary trees with choosable edge lengths

Authors:
Jens Maßberg;Dieter Rautenbach
Affiliations:
Forschungsinstitut für Diskrete Mathematik, Lennéstr. 2, 53113 Bonn, Germany;Institut für Mathematik, Technische Universität Ilmenau, Postfach 100565, D-98684 Ilmenau, Germany
Venue:
Information Processing Letters
Year:
2009

Citing 7
Cited 1

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Journal of the ACM (JACM)
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Abstract

For a set L@?(R"="02) of two-element sets of non-negative real numbers we consider rooted strict binary trees with the property that the two edges leading from every non-leaf to its two children are assigned lengths l"1 and l"2 with {l"1,l"2}@?L. For choices of L for which l"1+l"2 is constant for every {l"1,l"2}@?L which models that a certain total length can be distributed with some degree of freedom specified by L to incident edges, we study the asymptotic growth of the maximum number of leaves of bounded depths in such trees and the existence of such trees with leaves at individually specified maximum depths.