The optimal algorithm for dynamic support of the Voronoi Diagram for a set of points

2020 ◽  
pp. 63-68
Author(s):  
V. N. Tereshchenko ◽  
A. A. Marchenko ◽  
Y. V. Tereshchenko ◽  
A. N. Tara
Keyword(s):  
Data Structure ◽  
Voronoi Diagram ◽  
Optimal Algorithm ◽  
Original Algorithm ◽  
Dynamic Support ◽  
The Common ◽  
Divide And Rule ◽  
Dynamic Data Structure ◽  
Set Of Points ◽  
Red Black Tree

The article is devoted to the development of a dynamic data structure for solving proximity problems based on the dynamic Voronoi Diagram. This data structure can be used as the core of the common algorithmic space model for solving a set of visualization and computer modeling problems. The data structure is based on the strategy of "divide and rule" for Voronoi diagram construction. Similar to the original algorithm, we store a binary tree that represents the Voronoi diagram, but define three new operations: insert, delete, and balance. To ensure the efficiency of operations, it is proposed to use red-black tree. In general, the proposed data structure shows much better results than the original static algorithm. Compared to existing algorithms, this data structure is both simple and efficient.

scholarly journals Efficient Algorithms for Max-Weighted Point Sweep Coverage on Lines

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1457
Author(s):  
Dieyan Liang ◽  
Hong Shen
Keyword(s):  
Optimal Algorithm ◽  
Approximate Solutions ◽  
Approximation Ratio ◽  
Mobile Sensors ◽  
Np Hard ◽  
Coverage Problem ◽  
Polynomial Time Approximation Algorithm ◽  
Weighted Point ◽  
Eulerian Graph ◽  
Set Of Points

As an important application of wireless sensor networks (WSNs), deployment of mobile sensors to periodically monitor (sweep cover) a set of points of interest (PoIs) arises in various applications, such as environmental monitoring and data collection. For a set of PoIs in an Eulerian graph, the point sweep coverage problem of deploying the fewest sensors to periodically cover a set of PoIs is known to be Non-deterministic Polynomial Hard (NP-hard), even if all sensors have the same velocity. In this paper, we consider the problem of finding the set of PoIs on a line periodically covered by a given set of mobile sensors that has the maximum sum of weight. The problem is first proven NP-hard when sensors are with different velocities in this paper. Optimal and approximate solutions are also presented for sensors with the same and different velocities, respectively. For M sensors and N PoIs, the optimal algorithm for the case when sensors are with the same velocity runs in O(MN) time; our polynomial-time approximation algorithm for the case when sensors have a constant number of velocities achieves approximation ratio 12; for the general case of arbitrary velocities, 12α and 12(1−1/e) approximation algorithms are presented, respectively, where integer α≥2 is the tradeoff factor between time complexity and approximation ratio.

Improving the Red-Black tree delete algorithm

2021 ◽  
Author(s):  
ZEGOUR Djamel Eddine
Keyword(s):  
Data Structure ◽  
Search Tree ◽  
Binary Search ◽  
Binary Search Tree ◽  
Search Performance ◽  
Running Time ◽  
Standard Algorithm ◽  
Color Changes ◽  
Red Black Tree ◽  
Symbol Tables

Abstract Today, Red-Black trees are becoming a popular data structure typically used to implement dictionaries, associative arrays, symbol tables within some compilers (C++, Java …) and many other systems. In this paper, we present an improvement of the delete algorithm of this kind of binary search tree. The proposed algorithm is very promising since it colors differently the tree while reducing color changes by a factor of about 29%. Moreover, the maintenance operations re-establishing Red-Black tree balance properties are reduced by a factor of about 11%. As a consequence, the proposed algorithm saves about 4% on running time when insert and delete operations are used together while conserving search performance of the standard algorithm.

The Optimal Design on Connection Order of Network in Hydraulic Manifold Block

2011 ◽  
Vol 201-203 ◽  
pp. 2190-2194
Author(s):  
Jun Jun Zhang ◽  
Ji Sheng Wang ◽  
Jiang Yong Wang ◽  
Gang Liu ◽  
Jie Wang
Keyword(s):  
Genetic Algorithm ◽  
Optimal Design ◽  
Genetic Manipulation ◽  
Optimal Algorithm ◽  
Single Point ◽  
Adaptive Mutation ◽  
Gene Encoding ◽  
Mutation Strategy ◽  
The Common

As one of the important questions in the design of hydraulic manifold block — connection order of network, give a solution based on genetic algorithm. Genetic algorithm is the common effective intelligent optimal algorithm and suitable for solving a large combinatorial optimal problems. Gene encoding of ordinal representation, single-point crossover strategy and adaptive mutation strategy are used in the design of genetic manipulation.

BASELINE BOUNDED HALF-PLANE VORONOI DIAGRAM

2013 ◽  
Vol 05 (03) ◽  
pp. 1350021 ◽  
Author(s):  
BING SU ◽  
YINFENG XU ◽  
BINHAI ZHU
Keyword(s):  
Voronoi Diagram ◽  
Half Plane ◽  
Line Segment ◽  
Euclidean Plane ◽  
Voronoi Region ◽  
Point Set ◽  
Set Of Points

Given a set of points P = {p1, p2, …, pn} in the Euclidean plane, with each point piassociated with a given direction vi∈ V. P(pi, vi) defines a half-plane and L(pi, vi) denotes the baseline that is perpendicular to viand passing through pi. Define a region dominated by piand vias a Baseline Bounded Half-Plane Voronoi Region, denoted as V or(pi, vi), if a point x ∈ V or(pi, vi), then (1) x ∈ P(pi, vi); (2) the line segment l(x, pi) does not cross any baseline; (3) if there is a point pj, such that x ∈ P(pj, vj), and the line segment l(x, pj) does not cross any baseline then d(x, pi) ≤ d(x, pj), j ≠ i. The Baseline Bounded Half-Plane Voronoi Diagram, denoted as V or(P, V), is the union of all V or(pi, vi). We show that V or(pi, vi) and V or(P, V) can be computed in O(n log n) and O(n2log n) time, respectively. For the heterogeneous point set, the same problem is also considered.

The Research for Extension Software Data Structure

2010 ◽  
Vol 121-122 ◽  
pp. 849-853
Author(s):  
Xiao Mao Wu ◽  
Hui Ming Guo ◽  
Yong Quan Yu
Keyword(s):  
Data Structure ◽  
Software Design ◽  
Element Model ◽  
Structure Model ◽  
The Common ◽  
Matter Element Model

In this paper, we analyze the data structure of design of matter-element model from the level of software design, combined with the features of the common used data structure and matter-element model in Extenics, finally propose a new data structure model, which adapt to computation, reasoning and transformation using matter-element model.

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.

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