An Improved Parallel Algorithm for Delaunay Triangulation on Distributed Memory Parallel Computers

Lee, Sang Yoon; Park, Chanik; Park, Chan-Mo

doi:10.1016/s0129-6264(01)00063-4

Cited by 16 publications

(14 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Using a distributed memory setting, they report speedups of up to 4.5 for clusters of 8 processing elements (PEs) and uniformly distributed points. Further studies on distributed memory machines are presented by Lee et al [17]. They partition the input according to paths of Delaunay edges obtained from a lower convex hull projection [4].…”

Section: Related Workmentioning

confidence: 99%

“…With ever increasing input sizes, research interest has shifted from sequential algorithms towards parallel ones [2,4,6,9,11,15], with shared memory parallelism for algorithms in two dimensions receiving most of the attention. Distributed memory algorithms however -as studied by Cignoni et al [9] and Lee et al [17] -are required to cope with triangulations exceeding the memory limitations of one machine.…”

Section: Introductionmentioning

confidence: 99%

“…Previous D&C DT algorithms suffer from a complex -often * Karlsruhe Institute of Technology, Institute for Theoretical Informatics, Algorithmics II. Email: {funke, sanders}@kit.edu sequential -divide or merge step [9,17]. We reduce the merging of two partial triangulations to re-triangulating a small subset of their vertices using the same parallel algorithm and combining the three triangulations via hash table lookups.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Parallel d-D Delaunay Triangulations in Shared and Distributed Memory

Funke

Sanders

2017

2017 Proceedings of the Ninteenth Workshop on Algorithm Engineering and Experiments (ALENEX)

View full text Add to dashboard Cite

Computing the Delaunay triangulation (DT) of a given point set in R D is one of the fundamental operations in computational geometry. In this paper we present a novel divide-and-conquer (D&C) algorithm that lends itself equally well to shared and distributed memory parallelism. While previous D&C algorithms generally suffer from a complex -often sequential -merge or divide step, we reduce the merging of two partial triangulations to re-triangulating a small subset of their vertices using the same parallel algorithm and combining the three triangulations via parallel hash table lookups. In experiments we achieve a reasonable speedup on shared memory machines and compare favorably to CGAL's three-dimensional parallel DT implementation on some inputs.In the distributed memory setting we show that our approach scales to 2048 processing elements, which allows us to compute 3-D DTs for inputs with billions of points.

show abstract

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Parallel d-D Delaunay Triangulations in Shared and Distributed Memory

Funke

Sanders

2017

2017 Proceedings of the Ninteenth Workshop on Algorithm Engineering and Experiments (ALENEX)

View full text Add to dashboard Cite

show abstract

“…Lee proposed a data partition divide and conquer strategy, combined with the projection method for D-TIN parallel algorithm (Lee, et al, 1997). This segmentation method can guarantee no boundaries recovery and continuous processing in the merger step.…”

Section: Overview Of D-tin Parallel Computingmentioning

confidence: 99%

Delaunay Triangulation Parallel Construction Method and Its Application in Map Generalization

Shen

Guo

et al. 2012

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

View full text Add to dashboard Cite

ABSTRACT:Delaunay triangulated irregular network (D-TIN) has been widely used in various fields and also played an increasingly important role on map generalization. But for massive data processing, current D-TIN algorithm is still not efficient enough to meet the requirements of map generalization. Data partitioning is an important step of parallel algorithm design. The load balance and efficiency of data partitioning is the precondition of improving parallel algorithm efficiency. For aggregated distributed point sets, the traditional Delaunay Triangulation parallel algorithm can't ensure the balance and the execution's efficiency of the partitioning result. The paper introduces a partitioning method using dynamic strips aiming to guarantee the computing load balance. We tested the speed-up of the D-TIN parallel algorithm using different type of point sets and the results of the experiments shows that the method of dynamic strips partitioning can help to get high and stable speed-up and the data distributional pattern and size has less influence to it. The paper realizes a mesh simplification algorithm based on parallel D-TIN and compares the efficiency based on parallel and serial D-TIN.

show abstract

“…Lee et al [30] combine Hardwick's approach [28] with the InCode algorithm [20]. The small variation is that their algorithm does not recursively subdivide the input points into two groups via a median line but subdivides them immediately (in one step) into several slabs.…”

Section: Construction Of the Delaunay Triangulationmentioning

confidence: 99%

Practically oriented parallel Delaunay triangulation in E2 for computers with shared memory

Kohout

Kolingerová

Žára

2004

Computers & Graphics

View full text Add to dashboard Cite

This paper describes two simple and efficient parallel algorithms for the construction of the Delaunay triangulation ðDTðSÞÞ in E 2 by randomized incremental insertion. The construction of the DTðSÞ is one of the fundamental problems in computer graphics. The proposed algorithms are designed for parallel systems several processors and with shared memory. Such a hardware configuration (especially the case with two-processors) became widely available in the last few years thanks to low prices at present, but there is still a lack of parallel algorithms that are simple to implement and efficient enough to be an attractive alternative to existing serial algorithms. We have implemented both new algorithms in C++ and tested them on workstations with up to four processors. Thanks to memory caching we noticed several times even super-linear speed-up compared with the reference sequential algorithm. r

show abstract

An Improved Parallel Algorithm for Delaunay Triangulation on Distributed Memory Parallel Computers

Cited by 16 publications

References 3 publications

Parallel d-D Delaunay Triangulations in Shared and Distributed Memory

Parallel d-D Delaunay Triangulations in Shared and Distributed Memory

Delaunay Triangulation Parallel Construction Method and Its Application in Map Generalization

Practically oriented parallel Delaunay triangulation in E2 for computers with shared memory

Contact Info

Product

Resources

About