A Parallelizing Method for Generation of Voronoi Diagram Using Contact Zone

2020 ◽  
Vol 1 (2) ◽  
pp. 159-175
Author(s):  
Yuuhi Okahana ◽  
Yusuke Gotoh
Keyword(s):  
Contact Zone ◽  
Voronoi Diagram ◽  
Processing Time ◽  
Voronoi Diagrams ◽  
Spatial Network ◽  
K Nearest Neighbor ◽  
Voronoi Regions ◽  
Knn Search ◽  
Conventional Methods ◽  
Network Environments

Due to the recent popularization of the Geographic Information System (GIS), spatial network environments that can display the changes of spatial axes on mobile devices are receiving great attention. In spatial network environments, since a query object that seeks location information selects several candidate target objects based on the search conditions, we often use a k-nearest neighbor (kNN) search, which seeks several target objects near the query object. However, since a kNN search needs to find the kNN by calculating the distance from the query to all the objects, the computational complexity might become too large based on the number of objects. To reduce this computation time in a kNN search, many researchers have proposed a search method that divides regions using a Voronoi diagram. However, since conventional methods generate Voronoi diagrams for objects in order, the processing time for generating Voronoi diagrams might become too large when the number of objects is increased. In this paper, we propose a generation method of the Voronoi diagram by parallelizing the generation of Voronoi regions using a contact zone. Our proposed method can reduce the processing time of generating the Voronoi diagram by generating Voronoi regions in parallel based on the number of targets. Our evaluation confirmed that the processing time under the proposed method was reduced about 15.9\% more than conventional methods that are not parallelized.

A proposition of querying scheme with network Voronoi diagram in bichromatic reverse k-nearest neighbor

2017 ◽  
Vol 13 (1) ◽  
pp. 62-75 ◽  
Author(s):  
Yusuke Gotoh ◽  
Chiori Okubo
Keyword(s):  
Voronoi Diagram ◽  
Design Methodology ◽  
Processing Time ◽  
Nearest Neighbor ◽  
Spatial Networks ◽  
K Nearest Neighbor ◽  
Influence Zone ◽  
Content Type ◽  
Future Direction ◽  
Practical Implications

Purpose This study aims to propose and evaluate a searching scheme for a bichromatic reverse k-nearest neighbor (BRkNN) that has objects and queries in spatial networks. In this proposed scheme, the author’s search for the BRkNN of the query using an influence zone for each object with a network Voronoi diagram (NVD). Design/methodology/approach The author’s analyze and evaluate the performance of the proposed searching scheme. Findings The contribution of this paper is that it confirmed that the proposed searching scheme gives shorter processing time than the conventional linear search. Research limitations/implications A future direction of this study will involve making a searching scheme that reduces the processing time when objects move automatically on spatial networks. Practical implications In BRkNN, consider two groups in a convenience store, where several convenience stores, which are constructed in Groups A and B, operate in a given region. The author’s can use RNN is RkNN when k = 1 (RNN) effectively to set a new store considering the Euclidean and road distances among stores and the location relationship between Groups A and B. Originality/value In the proposed searching scheme, the author’s search for the BRkNN of the query for each object with an NVD using the influence zone, which is the region where an object in the spatial network recognizes the nearest neighbor for the query.

A SIMPLE ON-LINE RANDOMIZED INCREMENTAL ALGORITHM FOR COMPUTING HIGHER ORDER VORONOI DIAGRAMS

1992 ◽  
Vol 02 (04) ◽  
pp. 363-381 ◽  
Author(s):  
FRANZ AURENHAMMER ◽  
OTFRIED SCHWARZKOPF
Keyword(s):  
Voronoi Diagram ◽  
Structural Changes ◽  
Nearest Neighbor ◽  
Voronoi Diagrams ◽  
Simple Algorithm ◽  
Incremental Algorithm ◽  
K Nearest Neighbor ◽  
On Line ◽  
Incremental Construction ◽  
Primal Space

We present a simple algorithm for maintaining order-k Voronoi diagrams in the plane. By using a duality transform that is of interest in its own right, we show that the insertion or deletion of a site involves little more than the construction of a single convex hull in three-space. In particular, the order-k Voronoi diagram for n sites can be computed in time [Formula: see text] and optimal space [Formula: see text] by an on-line randomized incremental algorithm. The time bound can be improved by a logarithmic factor without losing much simplicity. For k≥ log 2 n, this is optimal for a randomized incremental construction; we show that the expected number of structural changes during the construction is ⊝(nk2). Finally, by going back to primal space, we obtain a dynamic data structure that supports k-nearest neighbor queries, insertions, and deletions in a planar set of sites. The structure promises easy implementation, exhibits a satisfactory expected performance, and occupies no more storage than the current order-k Voronoi diagram.

scholarly journals Design and Analysis System of KNN and ID3 Algorithm for Music Classification based on Mood Feature Extraction

2017 ◽  
Vol 7 (1) ◽  
pp. 486
Author(s):  
Made Sudarma ◽  
I Gede Harsemadi
Keyword(s):  
Feature Extraction ◽  
Processing Time ◽  
Nearest Neighbor ◽  
Extraction Process ◽  
Performance Comparison ◽  
K Nearest Neighbor ◽  
K Value ◽  
Id3 Algorithm ◽  
Analysis System ◽  
Music Information

Each of music which has been created, has its own mood which is emitted, therefore, there has been many researches in Music Information Retrieval (MIR) field that has been done for recognition of mood to music.  This research produced software to classify music to the mood by using K-Nearest Neighbor and ID3 algorithm.  In this research accuracy performance comparison and measurement of average classification time is carried out which is obtained based on the value produced from music feature extraction process.  For music feature extraction process it uses 9 types of spectral analysis, consists of 400 practicing data and 400 testing data.  The system produced outcome as classification label of mood type those are contentment, exuberance, depression and anxious.  Classification by using algorithm of KNN is good enough that is 86.55% at k value = 3 and average processing time is 0.01021.  Whereas by using ID3 it results accuracy of 59.33% and average of processing time is 0.05091 second.

CHEMICAL TESSELLATIONS — RESULTS OF BINARY AND TERTIARY REACTIONS BETWEEN METAL IONS AND FERRICYANIDE OR FERROCYANIDE LOADED GELS

2010 ◽  
Vol 20 (07) ◽  
pp. 2241-2252 ◽  
Author(s):  
B. P. J. DE LACY COSTELLO ◽  
I. JAHAN ◽  
P. HAMBIDGE ◽  
K. LOCKING ◽  
D. PATEL ◽  
...  
Keyword(s):  
Metal Ions ◽  
Voronoi Diagram ◽  
Metal Salt ◽  
Voronoi Diagrams ◽  
Reaction Rates ◽  
Cross Reactivity ◽  
Diffusion Reaction ◽  
Reactive Metal ◽  
Simple Chemical ◽  
Pattern Forming

In our recent letter [de Lacy Costello et al., 2009] we described the formation of spontaneous complex tessellations of the plane constructed in simple chemical reactions between drops of metal salts and ferricyanide or ferrocyanide loaded gels. In this paper, we provide more examples of binary tessellations and extend our analysis to tessellations constructed via tertiary mixtures of reactants. We also provide a classification system which describes the tessellation based on the reactivity of the metal salt with the substrate and also the cross-reactivity of the primary products. This results in balanced tessellations where both reactants have equal reactivity or unbalanced tessellations where one reactant has a lower reactivity with the gel. The products can also be partially or fully cross reactive which gives a highly complex tessellation. The tessellations are made up of colored cells (corresponding to different metal ferricyanides or ferrocyanides) separated by bisectors of low precipitate concentration. The tessellations constructed by these reactions constitute generalized Voronoi diagrams. In the case of certain binary or tertiary combinations of reactants where the diffusion/reaction rates differ, then multiplicatively weighted crystal growth Voronoi diagrams are constructed. Where one reactant has limited or no reactivity with the gel (or the products are cross reactive) then the fronts originating from the reactive metal ions cross the fronts originating from the partially reactive metal ions. The fronts can annihilate in the formation of a second Voronoi diagram relating to the relative positions of the reactive drops. Therefore, two or more generalised or weighted Voronoi diagrams can be calculated in parallel by these simple chemical systems. However when these reactions were used to calculate an additively weighted Voronoi diagram (the reaction was initiated at different time intervals) the diagram constructed did not correspond to the theoretical calculation. We use the failure of these reactions to construct an additively weighted Voronoi diagram to prove a mechanism of substrate competition for bisector formation. These tessellations are an important class of pattern forming reactions and are useful in modeling natural pattern forming phenomena in addition to being a great resource for scientific demonstrations.

Parallel kNN Queries for Big Data Based on Voronoi Diagram Using MapReduce

2015 ◽  
pp. 392-414
Author(s):  
Wei Yan
Keyword(s):  
Big Data ◽  
Voronoi Diagram ◽  
Spatial Databases ◽  
Nearest Neighbor ◽  
Programming Model ◽  
Dimensional Space ◽  
Data Sets ◽  
Two Dimensional ◽  
K Nearest Neighbor ◽  
K Nearest Neighbors

In cloud computing environments parallel kNN queries for big data is an important issue. The k nearest neighbor queries (kNN queries), designed to find k nearest neighbors from a dataset S for every object in another dataset R, is a primitive operator widely adopted by many applications including knowledge discovery, data mining, and spatial databases. This chapter proposes a parallel method of kNN queries for big data using MapReduce programming model. Firstly, this chapter proposes an approximate algorithm that is based on mapping multi-dimensional data sets into two-dimensional data sets, and transforming kNN queries into a sequence of two-dimensional point searches. Then, in two-dimensional space this chapter proposes a partitioning method using Voronoi diagram, which incorporates the Voronoi diagram into R-tree. Furthermore, this chapter proposes an efficient algorithm for processing kNN queries based on R-tree using MapReduce programming model. Finally, this chapter presents the results of extensive experimental evaluations which indicate efficiency of the proposed approach.

eDAR Algorithm for Continuous KNN Queries Based on Pine

2011 ◽  
pp. 154-174
Author(s):  
Maytham Safar ◽  
Dariush Ebrahimi
Keyword(s):  
Shortest Path ◽  
Nearest Neighbor ◽  
Query Point ◽  
Spatial Network ◽  
K Nearest Neighbor ◽  
Network Expansion ◽  
Shortest Distance ◽  
Stationary Objects ◽  
Split Point ◽  
Euclidean Distances

The continuous K nearest neighbor (CKNN) query is an important type of query that finds continuously the KNN to a query point on a given path. We focus on moving queries issued on stationary objects in Spatial Network Database (SNDB) The result of this type of query is a set of intervals (defined by split points) and their corresponding KNNs. This means that the KNN of an object traveling on one interval of the path remains the same all through that interval, until it reaches a split point where its KNNs change. Existing methods for CKNN are based on Euclidean distances. In this paper we propose a new algorithm for answering CKNN in SNDB where the important measure for the shortest path is network distances rather than Euclidean distances. We propose DAR and eDAR algorithms to address CKNN queries based on the progressive incremental network expansion (PINE) technique. Our experiments show that the eDAR approach has better response time, and requires fewer shortest distance computations and KNN queries than approaches that are based on VN3 using IE.

Research on the Repeater Optimization Based on Voronoi Model

2012 ◽  
Vol 588-589 ◽  
pp. 802-805
Author(s):  
Ban Teng Liu ◽  
Xi Lin Hu ◽  
Zheng Yu Xu ◽  
Yao Lin Liu ◽  
You Rong Chen
Keyword(s):  
Cellular Networks ◽  
Voronoi Diagram ◽  
Iterative Refinement ◽  
Local Optimum ◽  
Limited Capacity ◽  
Circular Area ◽  
Absolute Minimum ◽  
Voronoi Regions ◽  
Refinement Algorithm ◽  
Better Than

This paper propose a two-tiered network in which lower-power users communicate with one another through repeaters, which amplify signals and retransmit them, have limited capacity, and may interfere with one another if their transmitter frequencies are close and they share the same private-line tone. Motivated by cellular networks, this paper gives a naive solution where the number of repeaters and their positions can be obtained analytically. In a circular area with radius 40 miles, 12 repeaters can accommodate 1,000 simultaneous users. This paper further propose an iterative refinement algorithm consisting of three fundamental modules that draw the Voronoi diagram, determine the centers of the circumscribed circles of the Voronoi regions, and escape the local optimum by using external optimization. The algorithm obtains a solution with 11 repeaters, which we prove to be the absolute minimum. For 10,000 users, it uses 104 repeaters, better than the naive solution's 108.

scholarly journals Computation of Compact Distributions of Discrete Elements

Algorithms ◽  
2019 ◽  
Vol 12 (2) ◽  
pp. 41
Author(s):  
Jie Chen ◽  
Gang Yang ◽  
Meng Yang
Keyword(s):  
Voronoi Diagram ◽  
Compact Element ◽  
Synthesis Process ◽  
Distribution Area ◽  
Generation Process ◽  
Discrete Elements ◽  
Pattern Synthesis ◽  
Daily Lives ◽  
Voronoi Regions ◽  
Classic Pattern

In our daily lives, many plane patterns can actually be regarded as a compact distribution of a number of elements with certain shapes, like the classic pattern mosaic. In order to synthesize this kind of pattern, the basic problem is, with given graphics elements with certain shapes, to distribute a large number of these elements within a plane region in a possibly random and compact way. It is not easy to achieve this because it not only involves complicated adjacency calculations, but also is closely related to the shape of the elements. This paper attempts to propose an approach that can effectively and quickly synthesize compact distributions of elements of a variety of shapes. The primary idea is that with the seed points and distribution region given as premise, the generation of the Centroidal Voronoi Tesselation (CVT) of this region by iterative relaxation and the CVT will partition the distribution area into small regions of Voronoi, with each region representing the space of an element, to achieve a compact distribution of all the elements. In the generation process of Voronoi diagram, we adopt various distance metrics to control the shape of the generated Voronoi regions, and finally achieve the compact element distributions of different shapes. Additionally, approaches are introduced to control the sizes and directions of the Voronoi regions to generate element distributions with size and direction variations during the Voronoi diagram generation process to enrich the effect of compact element distributions. Moreover, to increase the synthesis efficiency, the time-consuming Voronoi diagram generation process was converted into a graphical rendering process, thus increasing the speed of the synthesis process. This paper is an exploration of elements compact distribution and also carries application value in the fields like mosaic pattern synthesis.

Discrete Construction of Compoundly Weighted Voronoi Diagram

2013 ◽  
Vol 467 ◽  
pp. 545-548
Author(s):  
Hui Wang
Keyword(s):  
Production Process ◽  
Voronoi Diagram ◽  
Voronoi Diagrams ◽  
High Potential ◽  
Graphic Display ◽  
Potential Value ◽  
Discrete Algorithms ◽  
Traditional Algorithm ◽  
Definition Of

Compoundly weighted Voronoi diagram is difficult to construct because the bisector is fairly complex. In traditional algorithm, production process is always extremely complex and it is more difficult to graphic display because of the complex definition of mathematic formula. In this paper, discrete algorithms are used to construct compoundly weighted Voronoi diagrams. The algorithm can get over all kinds of shortcomings that we have just mentioned. So it is more useful and effective than the traditional algorithm. The results show that the algorithm is both simple and useful, and it is of high potential value in practice.

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