Solving nearest neighbors problem on GPU to speed up the Fruchterman-Reingold graph layout algorithm

Uher, Vojtěch; Gajdoš, Petr; Ježowicz, Tomáš

doi:10.1109/cybconf.2015.7175951

Cited by 7 publications

(5 citation statements)

References 11 publications

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“…The simplified sparse structure is based on the idea of space filling curves (e.g. [12,20]). The hexagonal coordinates of clusters are converted to hash codes defining their cluster order on the SFC (Fig.…”

Section: Building Of Searching Structurementioning

confidence: 99%

“…The aim of this paper was to find a straightforward method for searching the k-NN to avoid unnecessary computations and memory accesses. We presented a similar method in [12] based on a level indexing of surrounding quads and used it for a parallel computation of neighborhood. The orthogonal grid can be easily computed and stored in a memory, but a neighborhood is circular, thus many quads have to be checked and eliminated.…”

mentioning

confidence: 99%

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Application of Hexagonal Coordinate Systems for Searching the K-NN in 2D Space

Uher

Gajdoš

Ježowicz

et al. 2015

Advances in Intelligent Systems and Computing

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Efficient searching of the k-nearest neighbors (k-NN) is a widely discussed problem. Most of the known 2D methods is based on division of a space to some quads or rectangular clusters. It is convenient for simple orthogonal querying of the space. However, a radius of neighbourhood is circular, thus the non complying quads have to be eliminated. This paper describes a novel approach of searching k-NN using hexagonal clustering of the 2D unordered point clouds. The hexagonal grid fully fills the 2D space as well. The shape of a hexagon is closer to the circular one and hexagonal coordinate systems are efficiently used to simply address the surrounding hexagons intersected by neighbourhood of a point. The paper contains performance tests of the proposed algorithm.Keywords k-nearest neighbors ⋅ k-NN ⋅ Hexagon ⋅ Hexagonal grid ⋅ Hexagonal coordinate system ⋅ Point cloud Related WorkThe k-NN problem solves the searching of the k closest points from a query point in an unordered point cloud (PC). A condition of a maximum radius of the neighborhood can be added. The k-NN is an important part of many algorithms like clustering, classification and generally machine learning algorithms. It can be applied

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Section: Building Of Searching Structurementioning

confidence: 99%

mentioning

confidence: 99%

Application of Hexagonal Coordinate Systems for Searching the K-NN in 2D Space

Uher

Gajdoš

Ježowicz

et al. 2015

Advances in Intelligent Systems and Computing

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“…SFCs are very straightforward and efficient methods for sparse-space clustering. Such a structure design is also much more convenient for massive parallel processing of clusters [4,5,12,13,53].…”

Section: Space-filling Curvesmentioning

confidence: 99%

“…Octree) instead of a sequential particle insertion [53]. Papers [12,13] discuss the utilization of SFCs for speeding up the nearest neighbors (NNs) algorithm and real time graph layout visualization. To bring a solid hexagonal method, we define the general criteria for good SFCs [1] in Section 2.2.…”

Section: Space-filling Curvesmentioning

confidence: 99%

“…A point cloud (PC) is a collection of points of the same type (2-3D real points) [9] representing a discrete form of real objects. Beside traditional PCs produced mostly by 3D scanners [9], a set of points can also represent general spatial information [10] such as location, GPS coordinates on the map [11], swarm particles [12], nodes of graph generated by visualization algorithms [13], etc. We focus on 2D point clouds as they are highly investigated in the areas such as data mining [2,3,10], computer graphics [14,15], image analysis [16][17][18], geographic information systems (GISs) [19][20][21][22][23], sensor networks [24,25], triangulation [26][27][28][29] and data visualization [12].…”

Section: Introductionmentioning

confidence: 99%

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Hierarchical Hexagonal Clustering and Indexing

et al. 2019

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Space-filling curves (SFCs) represent an efficient and straightforward method for sparse-space indexing to transform an n-dimensional space into a one-dimensional representation. This is often applied for multidimensional point indexing which brings a better perspective for data analysis, visualization and queries. SFCs are involved in many areas such as big data analysis and visualization, image decomposition, computer graphics and geographic information systems (GISs). The indexing methods subdivide the space into logic clusters of close points and they differ in various parameters including the cluster order, the distance metrics, and the pattern shape. Beside the simple and highly preferred triangular and square uniform grids, the hexagonal uniform grids have gained high interest especially in areas such as GISs, image processing and data visualization for the uniform distance between cells and high effectiveness of circle coverage. While the linearization of hexagons is an obvious approach for memory representation, it seems there is no hexagonal SFC indexing method generally used in practice. The main limitation of hexagons lies in lacking infinite decomposition into sub-hexagons and similarity of tiles on different levels of hierarchy. Our research aims at defining a fast and robust hexagonal SFC method. The Gosper fractal is utilized to preserve the benefits of hexagonal grids and to efficiently and hierarchically linearize points in a hexagonal grid while solving the non-convex shape and recursive transformation issues of the fractal. A comparison to other SFCs and grids is conducted to verify the robustness and effectiveness of our hexagonal method.

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