On the Size of Some Trees Embedded in Rd - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Reports (Research Report) Year : 2010

On the Size of Some Trees Embedded in Rd

Abstract

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].
Fichier principal
Vignette du fichier
RR-7179.pdf (234.27 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

inria-00448335 , version 1 (18-01-2010)

Identifiers

  • HAL Id : inria-00448335 , version 1

Cite

Pedro Machado Manhães de Castro, Olivier Devillers. On the Size of Some Trees Embedded in Rd. [Research Report] RR-7179, INRIA. 2010. ⟨inria-00448335⟩
180 View
96 Download

Share

Gmail Facebook Twitter LinkedIn More