Fast randomized point location without preprocessing in two- and three-dimensional Delaunay triangulations

Mücke, Ernst P.; Saias, Isaac; Zhu, Binhai

doi:10.1016/s0925-7721(98)00035-2

Cited by 63 publications

(65 citation statements)

References 18 publications

(40 reference statements)

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“…This "point location problem", which is a standard problem in geographic information systems and computer-aided design and engineering [74], is the most time consuming part. However, the number of tagged elements (which are cut by the slice plane) is usually far smaller than the total number of elements, and so we can use a brute force yet clever approach, which takes advantage of some peculiarities of our specific problem.…”

Section: Data Outputmentioning

confidence: 99%

Scalable parallel micromagnetic solvers for magnetic nanostructures

Scholz

Fidler

Schrefl

et al. 2003

Computational Materials Science

267

140

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Section: Data Outputmentioning

confidence: 99%

Scalable parallel micromagnetic solvers for magnetic nanostructures

Scholz

Fidler

Schrefl

et al. 2003

Computational Materials Science

267

140

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“…The first application is the randomized incremental construction of the Delaunay Triangulation using the Jump-andWalk strategy, introduced by Mücke, Zhu et al [12], [13]. This strategy proceeds in an incremental way.…”

Section: Convex Hull (2d-hull) and The Construction Of The Twodimensmentioning

confidence: 99%

Robust thread-level speculation

García-Yágüez

Llanos

González-Escribano

2011

2011 18th International Conference on High Performance Computing

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Robustness is a key issue on any runtime system that aims to speed up the execution of a program. However, robustness considerations are commonly overlooked when new software-based, thread-level speculation (STLS) systems are proposed. This paper highlights the relevance of the problem, showing different situations when the use of incorrect data can irreversibly alter the speculative execution of an algorithm, despite the efforts of a given STLS system to maintain sequential consistency. We show that the management of speculative exceptions is a common factor to these problems. Based on this fact, we propose a novel solution to handle speculative exceptions. Our solution eagerly tries to solve the issue before the non-speculative thread arrives to the instruction that rose the exception. We compare our solution to a more conservative approach found in the bibliography. The comparison is done both qualitatively, through a detailed analysis of the tradeoffs involved, and quantitatively, evaluating the effects of both solutions in the execution of three different benchmarks on a real system. Both studies conclude that our solution handles the occurrence of speculative exceptions more efficiently. Under heavy loads intended to push to its limits a STLS system, our solution leads to execution times reduced by up to 52.02% with respect to earlier proposals. Our solution does not affect the performance when speculative exceptions do not appear. We believe that our proposal makes STLS systems robust enough to be used in production environments.

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“…To know the value of a given attribute at a location x, one simply has to find the cell containing x- Mücke et al (1999) describe an efficient way to achieving that.…”

Section: Spatial Interpolationmentioning

confidence: 99%

Modelling three‐dimensional geoscientific fields with the Voronoi diagram and its dual

Ledoux

Gold

2008

International Journal of Geographical Information Science

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Fields as found in the geosciences have properties that are not usually found in other disciplines: the phenomena studied are often three-dimensional, they tend to change continuously over time, and the collection of samples to study the phenomena is problematic, which often results in highly anisotropic distributions of samples. In the GIS community, raster structures (voxels or octrees) are the most popular solutions, but, as we show in this paper, they have shortcomings for modelling and analysing 3D geoscientific fields. As an alternative to using rasters, we propose a new spatial model based on the Voronoi diagram (VD) and its dual the Delaunay tetrahedralization (DT), and argue that they have many advantages over other tessellations. We discuss the main properties of the 3D VD/DT, present some GIS operations that are greatly simplified when the VD/DT is used, and, to analyse two or more fields, we also present a variant of the map algebra framework where all the operations are performed directly on VDs. The usefulness of this Voronoi-based spatial model is demonstrated with a series of potential applications.

show abstract

Fast randomized point location without preprocessing in two- and three-dimensional Delaunay triangulations

Cited by 63 publications

References 18 publications

Scalable parallel micromagnetic solvers for magnetic nanostructures

Scalable parallel micromagnetic solvers for magnetic nanostructures

Robust thread-level speculation

Modelling three‐dimensional geoscientific fields with the Voronoi diagram and its dual

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