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Reports (Research Report) Year : 2010

On the Size of Some Trees Embedded in Rd


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


  • HAL Id : inria-00448335 , version 1


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