Geometric Algorithms for Finding a Point in the Intersection of Balls

We consider a problem of finding a point in the intersection of n balls in the Euclidean space E m . For the case m = 2 we suggest two algorithms of the complexity O ( n 2 log n ) and O ( n 3 ) operations, respectively. For the general case we suggest an exact polynomial recursive algorithm which us...

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Bibliographic Details
Published inAutomation and remote control Vol. 81; no. 5; pp. 869 - 882
Main Author Lushchakova, I. N.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.05.2020
Springer Nature B.V
Subjects
Algorithms
CAE) and Design
Calculus of Variations and Optimal Control; Optimization
Computer-Aided Engineering (CAD
Control
Euclidean geometry
Euclidean space
Geometric algorithms
Mathematics
Mathematics and Statistics
Mechanical Engineering
Mechatronics
Polynomials
Robotics
Systems Theory
Topical Issue
delivery applications of drones
polynomial algorithm
intersection of balls
approximation a convex set by ellipsoids
configuration of the swarm of drones
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ISSN0005-1179
1608-3032
DOI10.1134/S0005117920050070

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Summary:We consider a problem of finding a point in the intersection of n balls in the Euclidean space E m . For the case m = 2 we suggest two algorithms of the complexity O ( n 2 log n ) and O ( n 3 ) operations, respectively. For the general case we suggest an exact polynomial recursive algorithm which uses the orthogonal transformation of the space E m .
Bibliography:ObjectType-Article-1
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ISSN:0005-1179
1608-3032
DOI:10.1134/S0005117920050070