TWO-DIMENSIONAL RANGE SEARCH BASED ON THE VORONOI DIAGRAM

2005 ◽  
Vol 15 (02) ◽  
pp. 151-166
Author(s):  
TAKESHI KANDA ◽  
KOKICHI SUGIHARA
Keyword(s):  
Voronoi Diagram ◽  
Dimensional Space ◽  
Search Problem ◽  
Two Dimensional ◽  
Worst Case ◽  
Average Case ◽  
Range Search ◽  
Almost All ◽  
Set Of Points ◽  
Dimensional Range

This paper studies the two-dimensional range search problem, and constructs a simple and efficient algorithm based on the Voronoi diagram. In this problem, a set of points and a query range are given, and we want to enumerate all the points which are inside the query range as quickly as possible. In most of the previous researches on this problem, the shape of the query range is restricted to particular ones such as circles, rectangles and triangles, and the improvement on the worst-case performance has been pursued. On the other hand, the algorithm proposed in this paper is designed for a general shape of the query range in the two-dimensional space, and is intended to accomplish a good average-case performance. This performance is actually observed by numerical experiments. In these experiments, we compare the execution time of the proposed algorithm with those of other representative algorithms such as those based on the bucketing technique and the k-d tree. We can observe that our algorithm shows the better performance in almost all the cases.

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.

On the functional complexity of a two-dimensional interval search problem

2002 ◽  
Vol 12 (1) ◽  
Author(s):  
E.E. Gasanov ◽  
I.V. Kuznetsova
Keyword(s):  
Search Time ◽  
Search Problem ◽  
Two Dimensional ◽  
Worst Case ◽  
Logarithmic Average ◽  
Functional Complexity

AbstractWe suggest a modification of the Bentley-Maurer algorithm which solves a twodimensional interval search problem. This modification allows us to decrease the initially logarithmic average search time to constant, retaining the logarithmic worst-case search time. This algorithm depends on a parameter whose change results in variation of the needed memory from Ϭ(k

scholarly journals Worst-case & average-case Efficiency trade-offs for search problems

2021 ◽  
Author(s):  
Preeti Sharma
Keyword(s):  
Search Problem ◽  
Worst Case ◽  
Evacuation Time ◽  
Average Case ◽  
Deterministic Algorithms ◽  
Trade Offs ◽  
Time Work ◽  
Research Problems ◽  
Work Done ◽  
Vast Area

Evacuation problems fall under the vast area of search theory and operations research. Problems of evacuation of two robots on a unit disc have been studied for an efficient evacuation time. Work done so far has focused on improving the ’worst-case’ evacuation time with deterministic algorithms. We study the ’average-case’ evacuation time (randomized algorithms) while considering the efficiency trade-off between worst-case and average-case costs. Our other contribution is to analyze average-case and worst-case costs for the cowpath problem (another search problem) which helped us to set a parallel method for the evacuation problem.

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

2016 ◽  
pp. 644-665
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.

scholarly journals On the Most Likely Voronoi Diagram and Nearest Neighbor Searching

2016 ◽  
Vol 26 (03n04) ◽  
pp. 151-166 ◽  
Author(s):  
Subhash Suri ◽  
Kevin Verbeek
Keyword(s):  
Voronoi Diagram ◽  
Nearest Neighbor ◽  
Dimensional Space ◽  
Query Point ◽  
Worst Case ◽  
Smoothed Analysis ◽  
Bounded Number ◽  
Nearest Neighbor Searching ◽  
Space Data ◽  
Analysis Models

Let [Formula: see text] be a set of stochastic sites, where each site is a tuple [Formula: see text] consisting of a point [Formula: see text] in [Formula: see text]-dimensional space and a probability [Formula: see text] of existence. Given a query point [Formula: see text], we define its most likely nearest neighbor (LNN) as the site with the largest probability of being [Formula: see text]’s nearest neighbor. The Most Likely Voronoi Diagram (LVD) of [Formula: see text] is a partition of the space into regions with the same LNN. We investigate the complexity of LVD in one dimension and show that it can have size [Formula: see text] in the worst-case. We then show that under non-adversarial conditions, the size of the [Formula: see text]-dimensional LVD is significantly smaller: (1) [Formula: see text] if the input has only [Formula: see text] distinct probability values, (2) [Formula: see text] on average, and (3) [Formula: see text] under smoothed analysis. We also describe a framework for LNN search using Pareto sets, which gives a linear-space data structure and sub-linear query time in 1D for average and smoothed analysis models as well as the worst-case with a bounded number of distinct probabilities. The Pareto-set framework is also applicable to multi-dimensional LNN search via reduction to a sequence of nearest neighbor and spherical range queries.

scholarly journals Worst-case & average-case Efficiency trade-offs for search problems

2021 ◽  
Author(s):  
Preeti Sharma
Keyword(s):  
Search Problem ◽  
Worst Case ◽  
Evacuation Time ◽  
Average Case ◽  
Deterministic Algorithms ◽  
Trade Offs ◽  
Time Work ◽  
Research Problems ◽  
Work Done ◽  
Vast Area

Evacuation problems fall under the vast area of search theory and operations research. Problems of evacuation of two robots on a unit disc have been studied for an efficient evacuation time. Work done so far has focused on improving the ’worst-case’ evacuation time with deterministic algorithms. We study the ’average-case’ evacuation time (randomized algorithms) while considering the efficiency trade-off between worst-case and average-case costs. Our other contribution is to analyze average-case and worst-case costs for the cowpath problem (another search problem) which helped us to set a parallel method for the evacuation problem.

Rule Based Classifiers for Suspect Detection from CCTV Footages

2020 ◽  
Vol 13 ◽  
Author(s):  
Sunil Pathak
Keyword(s):  
Answer Sheet ◽  
Normal Activity ◽  
Contact Detection ◽  
Accuracy Rate ◽  
Hand Detection ◽  
Worst Case ◽  
Average Case ◽  
The Face ◽  
Case Simulation ◽  
Material Exchange

Background: The significant work has been present to identify suspects, gathering information and examining any videos from CCTV Footage. This exploration work expects to recognize suspicious exercises, i.e. object trade, passage of another individual, peeping into other's answer sheet and individual trade from the video caught by a reconnaissance camera amid examinations. This requires the procedure of face acknowledgment, hand acknowledgment and distinguishing the contact between the face and hands of a similar individual and that among various people. Methods: Segmented frames has given as input to obtain foreground image with the help of Gaussian filtering and background modeling method. Suh foreground images has given to Activity Recognition model to detect normal activity or suspicious activity. Results: Accuracy rate, Precision and Recall are calculate for activities detection, contact detection for Best Case, Average Case and Worst Case. Simulation results are compare with performance parameter such as Material Exchange, Position Exchange, and Introduction of a new person, Face and Hand Detection and Multi Person Scenario. Conclusion: In this paper, a framework is prepared for suspect detection. This framework will absolutely realize an unrest in the field of security observation in the training area.

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