Cuts in Increasing Trees

Olivier Bodini Antoine Genitrini 1
1 APR - Algorithmes, Programmes et Résolution
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : Increasing trees have been extensively studied, since it is a simple model for many natural phenomena. Our paper focuses on sub-families of increasing trees. We measure the number of connected components obtained after having removed the nodes whose labels are smaller than a given value. This measure of cut-length allows, for example, to analyse in average an algorithm for tree-labelling. It is noticeable that we give exact formulae for the distribution of trees according to their size and cut-lengths. Our approach is based on a construction using grafting processes.
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Submitted on : Wednesday, October 14, 2015 - 5:23:01 PM
Last modification on : Thursday, March 21, 2019 - 12:59:01 PM

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Olivier Bodini, Antoine Genitrini. Cuts in Increasing Trees. 2015 the Twelfth Workshop on Analytic Algorithmics and Combinatorics (ANALCO), Jan 2015, San Diego, CA, United States. pp.66-77, ⟨10.1137/1.9781611973761.6⟩. ⟨hal-01215715⟩



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