scholarly journals TRIANGULATING A REGION BETWEEN ARBITRARY POLYGONS

2017 ◽  
pp. 160-165
Author(s):  
Vasyl Tereshchenko ◽  
Yaroslav Tereshchenko
Keyword(s):  
Data Structure ◽  
Convex Hull ◽  
Efficient Algorithm ◽  
Time Complexity ◽  
Optimal Algorithm ◽  
Simple Polygon ◽  
Overall Design ◽  
Simple Implementation ◽  
Monotone Polygons ◽  
Two Stages

The paper presents an optimal algorithm for triangulating a region between arbitrary polygons on the plane with time complexity O(N log⁡N ). An efficient algorithm is received by reducing the problem to the triangulation of simple polygons with holes. A simple polygon with holes is triangulated using the method of monotone chains and keeping overall design of the algorithm simple. The problem is solved in two stages. In the first stage a convex hull for m polygons is constructed by Graham’s method. As a result, a simple polygon with holes is received. Thus, the problem of triangulating a region between arbitrary polygons is reduced to the triangulation of a simple polygon with holes. In the next stage the simple polygon with holes is triangulated using an approach based on procedure of splitting polygon onto monotone polygons using the method of chains [15]. An efficient triangulating algorithm is received. The proposed algorithm is characterized by a very simple implementation, and the elements (triangles) of the resulting triangulation can be presented in the form of simple and fast data structure: a tree of triangles [17].

scholarly journals ALGORITHMS FOR DISTANCE PROBLEMS IN PLANAR COMPLEXES OF GLOBAL NONPOSITIVE CURVATURE

2014 ◽  
Vol 24 (01) ◽  
pp. 1-38 ◽  
Author(s):  
DANIELA MAFTULEAC
Keyword(s):  
Data Structure ◽  
Convex Hull ◽  
Metric Spaces ◽  
Linear Time ◽  
Single Point ◽  
Simple Polygon ◽  
Query Point ◽  
Planar Complex ◽  
Finite Set ◽  
Set Of Points

CAT(0) metric spaces and hyperbolic spaces play an important role in combinatorial and geometric group theory. In this paper, we present efficient algorithms for distance problems in CAT(0) planar complexes. First of all, we present an algorithm for answering single-point distance queries in a CAT(0) planar complex. Namely, we show that for a CAT(0) planar complex [Formula: see text] with n vertices, one can construct in O(n2 log n) time a data structure [Formula: see text] of size O(n2) so that, given a point [Formula: see text], the shortest path γ(x, y) between x and the query point y can be computed in linear time. Our second algorithm computes the convex hull of a finite set of points in a CAT(0) planar complex. This algorithm is based on Toussaint's algorithm for computing the convex hull of a finite set of points in a simple polygon and it constructs the convex hull of a set of k points in O(n2 log n + nk log k) time, using a data structure of size O(n2 + k).

FINDING THE LARGEST EMPTY DISK CONTAINING A QUERY POINT

2013 ◽  
Vol 23 (04n05) ◽  
pp. 335-355 ◽  
Author(s):  
HAIM KAPLAN ◽  
MICHA SHARIR
Keyword(s):  
Data Structure ◽  
Efficient Algorithm ◽  
Alternative Solution ◽  
Query Point

Let P be a set of n points in the plane. We present an efficient algorithm for preprocessing P, so that, for a given query point q, we can quickly report the largest disk that contains q but its interior is disjoint from P. The storage required by the data structure is O(n log n), the preprocessing cost is O(n log 2 n), and a query takes O( log 2 n) time. We also present an alternative solution with an improved query cost and with slightly worse storage and preprocessing requirements.

IMIDB: An Algorithm for Indexed Mining of Incremental Databases

2017 ◽  
Vol 26 (1) ◽  
pp. 69-85
Author(s):  
Mohammed M. Fouad ◽  
Mostafa G.M. Mostafa ◽  
Abdulfattah S. Mashat ◽  
Tarek F. Gharib
Keyword(s):  
Data Structure ◽  
Association Rules ◽  
Efficient Algorithm ◽  
Performance Comparison ◽  
Incremental Mining ◽  
Itemset Mining ◽  
Large Databases ◽  
Transactional Databases ◽  
Dynamic Databases ◽  
Database Size

AbstractAssociation rules provide important knowledge that can be extracted from transactional databases. Owing to the massive exchange of information nowadays, databases become dynamic and change rapidly and periodically: new transactions are added to the database and/or old transactions are updated or removed from the database. Incremental mining was introduced to overcome the problem of maintaining previously generated association rules in dynamic databases. In this paper, we propose an efficient algorithm (IMIDB) for incremental itemset mining in large databases. The algorithm utilizes the trie data structure for indexing dynamic database transactions. Performance comparison of the proposed algorithm to recently cited algorithms shows that a significant improvement of about two orders of magnitude is achieved by our algorithm. Also, the proposed algorithm exhibits linear scalability with respect to database size.

scholarly journals The importance of computational geometry for digital cartography

2008 ◽  
Vol 3 ◽  
pp. 15-24
Author(s):  
Tomáš Bayer
Keyword(s):  
Computational Geometry ◽  
Convex Hull ◽  
Time Complexity ◽  
Geometric Structures ◽  
Digital Cartography ◽  
Relationship Of ◽  
The Relationship

This paper describes the use of computational geometry concepts in the digital cartography.  It presents an importance of 2D geometric structures, geometric operations and procedures for automated or semi automated simplification process. This article is focused on automated building simplification procedures, some techniques are illustrated and discussed. Concrete examples with the requirements to the lowest time complexity, emphasis on the smallest area enclosing rectangle, convex hull or self intersection procedures, are given. Presented results illustrate the relationship of digital cartography and computational geometry.

scholarly journals Efficient Algorithm For L(3,2,1)-Labeling of Cartesian Product Between Some Graphs

10.29007/x3qf ◽  
2019 ◽  
Author(s):  
Sumonta Ghosh ◽  
Prakhar Pogde ◽  
Narayan C. Debnath ◽  
Anita Pal
Keyword(s):  
Communication Network ◽  
Assignment Problem ◽  
Efficient Algorithm ◽  
Time Complexity ◽  
Cartesian Product ◽  
Frequency Assignment ◽  
Frequency Assignment Problem ◽  
The Difference

L(h,k) Labeling in graph came into existence as a solution to frequency assignment problem. To reduce interference a frequency in the form of non negative integers is assigned to each radio or TV transmitters located at various places. After L(h,k) labeling, L(h,k, j) labeling is introduced to reduce noise in the communication network. We investigated the graph obtained by Cartesian Product betweenCompleteBipartiteGraphwithPathandCycle,i. e.,Km,n×Pr andKm,n×Cr byapplying L(3,2,1)Labeling. The L(3,2,1) Labeling of a graph G is the difference between the highest and the lowest labels used in L(3,2,1) and is denoted by λ3,2,1(G) In this paper we have designed three suitable algorithms to label the graphs Km,n × Pr and Km,n × Cr . We have also analyzed the time complexity of each algorithm with illustration.

An Efficient Algorithm for Automating Classification of Chemical Reactions into Classes in Ugi’s Reaction Scheme

2013 ◽  
pp. 285-296
Author(s):  
Sanjay Ram ◽  
Somnath Pal
Keyword(s):  
Chemical Reactions ◽  
Efficient Algorithm ◽  
Time Complexity ◽  
Symmetric Matrix ◽  
Reaction Scheme ◽  
Space Complexity ◽  
Average Case ◽  
Model Driven ◽  
Reaction Matrix

There are two approaches for classification of chemical reactions: Model-Driven and Data-Driven. In this paper, the authors develop an efficient algorithm based on a model-driven approach developed by Ugi and co-workers for classification of chemical reactions. The authors’ algorithm takes reaction matrix of a chemical reaction as input and generates its appropriate class as output. Reaction matrices being symmetric, matrix implementation of Ugi’s scheme using upper/lower tri-angular matrix is of O(n2) in terms of space complexity. Time complexity of similar matrix implementation is O(n4), both in worst case as well as in average case. The proposed algorithm uses two fixed size look-up tables in a novel way and requires constant space complexity. Time complexity both in worst and average cases of the algorithm is linear.

scholarly journals An Efficient Algorithm for Eigenvalue Problem of Latin Squares in a Bipartite Min-Max-Plus System

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 311 ◽  
Author(s):  
Mubasher Umer ◽  
Umar Hayat ◽  
Fazal Abbas ◽  
Anurag Agarwal ◽  
Petko Kitanov
Keyword(s):  
Eigenvalue Problem ◽  
Efficient Algorithm ◽  
Time Complexity ◽  
Latin Square ◽  
Latin Squares ◽  
Clear Advantage

In this paper, we consider the eigenproblems for Latin squares in a bipartite min-max-plus system. The focus is upon developing a new algorithm to compute the eigenvalue and eigenvectors (trivial and non-trivial) for Latin squares in a bipartite min-max-plus system. We illustrate the algorithm using some examples. The proposed algorithm is implemented in MATLAB, using max-plus algebra toolbox. Computationally speaking, our algorithm has a clear advantage over the power algorithm presented by Subiono and van der Woude. Because our algorithm takes 0 . 088783 sec to solve the eigenvalue problem for Latin square presented in Example 2, while the compared one takes 1 . 718662 sec for the same problem. Furthermore, a time complexity comparison is presented, which reveals that the proposed algorithm is less time consuming when compared with some of the existing algorithms.

A New Algorithm for Euclidean Shortest Path of Visiting Segments in a Polygon

2014 ◽  
Vol 644-650 ◽  
pp. 1891-1894
Author(s):  
Li Juan Wang ◽  
An Sheng Deng ◽  
Bo Jiang ◽  
Qi Wei
Keyword(s):  
Test Data ◽  
Shortest Path ◽  
Time Complexity ◽  
Simple Polygon ◽  
Rubber Band ◽  
Crossing Over ◽  
Euclidean Shortest Path ◽  
Adjacent Segments ◽  
Improved Algorithm

Let s and t be two points on the boundary of a simple polygon, how to compute the Euclidean shortest path between s and t which visits a sequence of segments given in the simple polygon is the problem to be discussed, especially, the situation of the adjacent segments intersect is the focus of our study. In this paper, we first analyze the degeneration applying rubber-band algorithm to solve the problem. Then based on rubber-band algorithm, we present an improved algorithm which can solve the degeneration by the method of crossing over two segments to deal with intersection and in our algorithm the adjacent segments order can be changed when they intersect. Particularly, we have implemented the algorithm and have applied a large of test data to test it. The experiments demonstrate that our algorithm is correct and efficient, and it has the same time complexity as the rubber-band algorithm.

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