Delaunay triangulation of large-scale datasets using two-level parallelism

Nguyen, Cuong M.; Rhodes, Philip J.

doi:10.1016/j.parco.2020.102672

Cited by 7 publications

(5 citation statements)

References 38 publications

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“…To tackle this problem, several hybrid algorithms that combine parallel and incremental approaches have been developed. These algorithms have been implemented on clusters, as described in [19], or on the cloud, as demonstrated in [20] and [17]. In the latter work, the authors compared the performance of a hybrid cloud-based algorithm with that of a sequential implementation on a single machine.…”

Section: ) Scaling Up To a Billion Pointsmentioning

confidence: 99%

A Comprehensive Survey on Delaunay Triangulation: Applications, Algorithms, and Implementations Over CPUs, GPUs, and FPGAs

Elshakhs,

Deliparaschos,

Charalambous

et al. 2024

IEEE Access

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Section: ) Scaling Up To a Billion Pointsmentioning

confidence: 99%

A Comprehensive Survey on Delaunay Triangulation: Applications, Algorithms, and Implementations Over CPUs, GPUs, and FPGAs

Elshakhs,

Deliparaschos,

Charalambous

et al. 2024

IEEE Access

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“…Many parallel Delaunay triangulation algorithms have been proposed. Most focus on partitioning the domain that contains the points so that each partition can be triangulated separately and in parallel with the others. − The bottleneck of this approach, however, is the merging of the triangulations from the different partitions to generate the complete triangulation . The tetrahedra at the borders of a partition have to be connected to tetrahedra in adjacent partitions, often leading to local retriangulations.…”

Section: Algorithm and Implementationmentioning

confidence: 99%

“…Of these three steps, the second and the third can be easily parallelized, as they basically involve iterating over simplices. Unfortunately, parallelizing the computation of the Delaunay triangulation is a difficult task that remains a hot topic in research. − Considering that computing the Delaunay triangulation is more than 50% of the total computing cost of AlphaMol (see Figure ), this is a concern.…”

Section: Algorithm and Implementationmentioning

confidence: 99%

Computing the Volume, Surface Area, Mean, and Gaussian Curvatures of Molecules and Their Derivatives

Koehl

Akopyan²,

Edelsbrunner

2023

J. Chem. Inf. Model.

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Geometry is crucial in our efforts to comprehend the structures and dynamics of biomolecules. For example, volume, surface area, and integrated mean and Gaussian curvature of the union of balls representing a molecule are used to quantify its interactions with the water surrounding it in the morphometric implicit solvent models. The Alpha Shape theory provides an accurate and reliable method for computing these geometric measures. In this paper, we derive homogeneous formulas for the expressions of these measures and their derivatives with respect to the atomic coordinates, and we provide algorithms that implement them into a new software package, AlphaMol. The only variables in these formulas are the interatomic distances, making them insensitive to translations and rotations. AlphaMol includes a sequential algorithm and a parallel algorithm. In the parallel version, we partition the atoms of the molecule of interest into 3D rectangular blocks, using a kd-tree algorithm. We then apply the sequential algorithm of AlphaMol to each block, augmented by a buffer zone to account for atoms whose ball representations may partially cover the block. The current parallel version of AlphaMol leads to a 20-fold speed-up compared to an independent serial implementation when using 32 processors. For instance, it takes 31 s to compute the geometric measures and derivatives of each atom in a viral capsid with more than 26 million atoms on 32 Intel processors running at 2.7 GHz. The presence of the buffer zones, however, leads to redundant computations, which ultimately limit the impact of using multiple processors. AlphaMol is available as an OpenSource software.

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“…The principle of DT is simple: for a given set P, any two points could construct an edge of DT map when there is a circle above two points and there is no other point in the circle [34].…”

Section: Delaunay Triangulationmentioning

confidence: 99%

A Novel Algorithm for Ship Route Planning Considering Motion Characteristics and ENC Vector Maps

Hou

Zhu

2023

JMSE

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Global route planning is a pivotal function of unmanned surface vehicles (USVs). For ships, the safety of navigation is the priority. This paper presents the VK-RRT* algorithm as a way of designing the planned route automatically. Different from other algorithms or studies, this study employs electronic navigation chart (ENC) vector data instead of grid maps as the basis of the search, which reduces data error when converting the vector map into the grid map. In addition, Delaunay triangulation is employed to organize vector data, in which the depth value is taken as a factor to ensure the safety of the planning route. Furthermore, the initial planned route is not suitable for ship tracking as it does not consider the ship motion characteristics. Therefore, the planned route needs to be further optimized. In the final part, we also conducted experiments to verify the effectiveness and advantages of the proposed algorithm. The results show that the proposed algorithm could reduce the lengths of paths by about 23% on average and save planning time; these are largely dependent on the environment.

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Delaunay triangulation of large-scale datasets using two-level parallelism

Cited by 7 publications

References 38 publications

A Comprehensive Survey on Delaunay Triangulation: Applications, Algorithms, and Implementations Over CPUs, GPUs, and FPGAs

A Comprehensive Survey on Delaunay Triangulation: Applications, Algorithms, and Implementations Over CPUs, GPUs, and FPGAs

Computing the Volume, Surface Area, Mean, and Gaussian Curvatures of Molecules and Their Derivatives

A Novel Algorithm for Ship Route Planning Considering Motion Characteristics and ENC Vector Maps

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