scholarly journals Properties of the Vacancy Statistic in the Discrete Circle Covering Problem

2013 ◽  
Author(s):  
Gadi Barlevy ◽  
H.N. Nagaraja
Keyword(s):  
Covering Problem ◽  
Circle Covering

Covering Discs in Minkowski Planes

2009 ◽  
Vol 52 (3) ◽  
pp. 424-434 ◽  
Author(s):  
Horst Martini ◽  
Margarita Spirova
Keyword(s):  
Essential Role ◽  
Covering Problem ◽  
Minkowski Geometry ◽  
Minkowski Planes ◽  
Strictly Convex ◽  
Unit Circles ◽  
Circle Covering ◽  
Monotonicity Lemma

AbstractWe investigate the following version of the circle covering problem in strictly convex (normed or) Minkowski planes: to cover a circle of largest possible diameter by k unit circles. In particular, we study the cases k = 3, k = 4, and k = 7. For k = 3 and k = 4, the diameters under consideration are described in terms of side-lengths and circumradii of certain inscribed regular triangles or quadrangles. This yields also simple explanations of geometric meanings that the corresponding homothety ratios have. It turns out that basic notions from Minkowski geometry play an essential role in our proofs, namely Minkowskian bisectors, d-segments, and the monotonicity lemma.

Single Facility Location: Circle Covering Problem

2008 ◽  
pp. 3607-3610
Author(s):  
Donald W. Hearn
Keyword(s):  
Facility Location ◽  
Covering Problem ◽  
Circle Covering ◽  
Single Facility

scholarly journals On reserve and double covering problems for the sets with non-Euclidean metrics

2019 ◽  
Vol 29 (1) ◽  
pp. 69-79
Author(s):  
Anna Lempert ◽  
Alexander Kazakov ◽  
Quang Le
Keyword(s):  
Convex Sets ◽  
Numerical Algorithms ◽  
Complex Problem ◽  
Covering Problem ◽  
Bounded Set ◽  
Euclidean Metrics ◽  
Circle Covering ◽  
Covering Set ◽  
Fundamental Physical ◽  
Physical Principles

The article is devoted to Circle covering problem for a bounded set in a two-dimensional metric space with a given amount of circles. Here we focus on a more complex problem of constructing reserve and multiply coverings. Besides that, we consider the case where covering set is a multiply-connected domain. The numerical algorithms based on fundamental physical principles, established by Fermat and Huygens, are suggested and implemented. This allows us to solve the problems for the cases of non-convex sets and non-Euclidean metrics. Preliminary results of numerical experiments are presented and discussed. Calculations show the applicability of the proposed approach.

scholarly journals A Parallel Interval Arithmetic-based Reliable Computing Method on a GPU

2017 ◽  
Vol 23 (2) ◽  
pp. 491-501 ◽  
Author(s):  
Zsolt Bagóczki ◽  
Balázs Bánhelyi
Keyword(s):  
Branch And Bound ◽  
High Speed ◽  
General Purpose ◽  
Three Dimensions ◽  
Direct Access ◽  
Covering Problem ◽  
Virtual Instruction ◽  
Wide Range ◽  
Circle Covering ◽  
Sphere Covering

Video cards have now outgrown their purpose of being only a simple tool for graphic display. With their high speed video memories, lots of maths units and parallelism, they can be very powerful accessories for general purpose computing tasks. Our selected platform for testing is the CUDA (Compute Unified Device Architecture), which offers us direct access to the virtual instruction set of the video card, and we are able to run our computations on dedicated computing kernels. The CUDA development kit comes with a useful toolbox and a wide range of GPU-based function libraries. In this parallel environment, we implemented a reliable method based on the Branch-and-Bound algorithm. This algorithm will give us the opportunity to use node level (also called low-level or type 1) parallelization, since we do not modify the searching trajectories; nor do we modify the dimensions of the Branch-and-Bound tree [5]. For testing, we chose the circle covering problem. We then scaled the problem up to three dimensions, and ran tests with sphere covering problems as well.

A circle covering problem and DNA breakage

1990 ◽  
Vol 9 (4) ◽  
pp. 295-298 ◽  
Author(s):  
Lars Holst
Keyword(s):  
Covering Problem ◽  
Dna Breakage ◽  
Circle Covering

Single Facility Location: Circle Covering Problem

2006 ◽  
pp. 2398-2401
Author(s):  
Donald W. Hearn
Keyword(s):  
Facility Location ◽  
Covering Problem ◽  
Circle Covering ◽  
Single Facility

A new approach using a Binary Firefly Algorithm for the Set Covering Problem

2014 ◽  
Author(s):  
Broderick Crawford ◽  
Ricardo Soto ◽  
Miguel Olivares-Suárez ◽  
Fernando Paredes
Keyword(s):  
Firefly Algorithm ◽  
Set Covering ◽  
Covering Problem ◽  
Set Covering Problem ◽  
New Approach

scholarly journals Q-Learnheuristics: Towards Data-Driven Balanced Metaheuristics

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1839
Author(s):  
Broderick Crawford ◽  
Ricardo Soto ◽  
José Lemus-Romani ◽  
Marcelo Becerra-Rozas ◽  
José M. Lanza-Gutiérrez ◽  
...  
Keyword(s):  
Combinatorial Problems ◽  
Set Covering ◽  
Covering Problem ◽  
Integration Framework ◽  
Q Learning ◽  
Whale Optimization ◽  
Sine Cosine Algorithm ◽  
Exploration Exploitation ◽  
Selection Of

One of the central issues that must be resolved for a metaheuristic optimization process to work well is the dilemma of the balance between exploration and exploitation. The metaheuristics (MH) that achieved this balance can be called balanced MH, where a Q-Learning (QL) integration framework was proposed for the selection of metaheuristic operators conducive to this balance, particularly the selection of binarization schemes when a continuous metaheuristic solves binary combinatorial problems. In this work the use of this framework is extended to other recent metaheuristics, demonstrating that the integration of QL in the selection of operators improves the exploration-exploitation balance. Specifically, the Whale Optimization Algorithm and the Sine-Cosine Algorithm are tested by solving the Set Covering Problem, showing statistical improvements in this balance and in the quality of the solutions.

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