On the asymptotic growth rate of some spanning trees embedded in

Castro, Pedro Machado Manhães de; Devillers, Olivier

doi:10.1016/j.orl.2010.10.005

Cited by 2 publications

(4 citation statements)

References 7 publications

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“…Finally, Steele shows that the growth rate of EM IT (S) is as large as the one of EM ST (S) [45] (this result has been recently generalized [13]). More precisely:…”

Section: On the Growth Rate Of Trees Inmentioning

confidence: 82%

“…Proofs of Theorems 4, 5, and 11 below are restricted cases of theorems proved in a companion paper [13].…”

Section: Constant-size-memory Strategiesmentioning

confidence: 99%

“…Theorem 11 ( [13], for α = 1). Let S be a sequence of m query-points uniformly independent and identically distributed in the unit ball, then the expected length of the Location Tree of the k-last-points strategy satisfies…”

Section: Theoremmentioning

confidence: 99%

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Practical distribution-sensitive point location in triangulations

Castro

Devillers

2013

Computer Aided Geometric Design

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We design, analyze, implement, and evaluate a distribution-sensitive point location algorithm based on the classical Jump & Walk, called Keep, Jump, & Walk. For a batch of query points, the main idea is to use previous queries to improve the current one. In practice, Keep, Jump, & Walk is actually a very competitive method to locate points in a triangulation. We also study some constantmemory distribution-sensitive point location algorithms, which work well in practice with the classical space-filling heuristic for fast point location. Regarding point location in a Delaunay triangulation, we show how the Delaunay hierarchy can be used to answer, under some hypotheses, a query q with a O(log #(pq)) randomized expected complexity, where p is a previously located query and #(s) indicates the number of simplices crossed by the line segment s. The Delaunay hierarchy has O(n log n) time complexity and O(n) memory complexity in the plane, and under certain realistic hypotheses these complexities generalize to any finite dimension. Finally, we combine the good distribution-sensitive behavior of Keep, Jump, & Walk, and the good complexity of the Delaunay hierarchy, into a novel point location algorithm called Keep, Jump, & Climb. To the best of our knowledge, Keep, Jump, & Climb is the first practical distribution-sensitive algorithm that works both in theory and in practice for Delaunay triangulations.

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“…Finally, Steele shows that the growth rate of EM IT (S) is as large as the one of EM ST (S) [45] (this result has been recently generalized [13]). More precisely:…”

Section: On the Growth Rate Of Trees Inmentioning

confidence: 82%

“…Proofs of Theorems 4, 5, and 11 below are restricted cases of theorems proved in a companion paper [13].…”

Section: Constant-size-memory Strategiesmentioning

confidence: 99%

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Practical distribution-sensitive point location in triangulations

Castro

Devillers

2013

Computer Aided Geometric Design

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“…( [9], for α = 1) Let S be a sequence of query points uniformly i.i.d in the unit ball, denoted by B unit , then the expected length of the k-th edge of EM IT (S) is such that …”

Section: Locationmentioning

confidence: 99%

Simple and Efficient Distribution-Sensitive Point Location in Triangulations

Castro

Devillers

2011

2011 Proceedings of the Thirteenth Workshop on Algorithm Engineering and Experiments (ALENEX)

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We analyze, implement, and evaluate a distributionsensitive point location algorithm based on the classical Jump & Walk, called Keep, Jump, & Walk. For a batch of query points, the main idea is to use previous queries to improve the current one. In practice, Keep, Jump, & Walk is actually a very competitive method to locate points in a triangulation. Regarding point location in a Delaunay triangulation, we show how the Delaunay hierarchy can be used to answer, under some hypotheses, a query q with a O(log #(pq)) randomized expected complexity, where p is a previously located query and #(s) indicates the number of simplices crossed by the line segment s. The Delaunay hierarchy has O(n log n) time complexity and O(n) memory complexity in the plane, and under certain realistic hypotheses these complexities generalize to any finite dimension. Finally, we combine the good distribution-sensitive behavior of Keep, Jump, & Walk, and the good complexity of the Delaunay hierarchy, into a novel point location algorithm called Keep, Jump, & Climb. To the best of our knowledge, Keep, Jump, & Climb is the first practical distributionsensitive algorithm that works both in theory and in practice for Delaunay triangulations.

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On the asymptotic growth rate of some spanning trees embedded in

Cited by 2 publications

References 7 publications

Practical distribution-sensitive point location in triangulations

Practical distribution-sensitive point location in triangulations

Simple and Efficient Distribution-Sensitive Point Location in Triangulations

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