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On the Size of Some Trees Embedded in Rd

Pedro Machado Manhaes De Castro 1, Olivier Devillers 1

(18/01/2010)

This paper extends the result of Steele [6,5] on the worst-case length of the Euclidean minimum spanning tree EMST and the Euclidean minimum insertion tree EMIT of a set of n points S contained in Rd. More precisely, we show that, if the weight w of an edge e is its Euclidean length to the power of α, the following quantities Σ_{e ∈ EMST} w(e) and Σ_{e ∈ EMIT} w(e) are both worst-case O(n^{1-α/d}), where d is the dimension and α, 0 < α < d, is the weight. Also, we analyze and compare the value of Σ_{e ∈ T} w(e) for some trees T embedded in Rd which are of interest in (but not limited to) the point location problem [2].

1 :	GEOMETRICA (INRIA Sophia Antipolis / INRIA Saclay - Ile de France)
	INRIA

Domaine

:

Informatique/Géométrie algorithmique

Mots-clés : Computational Geometry – Geometric Graphs

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Contributeur : Pedro Machado Manhaes De Castro <>

Soumis le : Lundi 18 Janvier 2010, 16:58:48

Dernière modification le : Vendredi 5 Février 2010, 13:15:46