Minimum area polygons with two reflex angles enclosing k Points

We present in this paper, algorithms for finding the minimum area isothetic polygons having two reflex angles containing k points; (k<n) Our algorithms are based on line sweep paradigm. The idea is to enumerate all the polygons in each kind and find the minimum one. We also analyse the complexiti...

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Veröffentlicht in:International journal of computer mathematics Jg. 77; H. 4; S. 507 - 522
Hauptverfasser: Krithivasan, Kamala, Srilakshmi, Vanam
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Abingdon Gordon and Breach Science Publishers 01.01.2001
Taylor and Francis
Schlagworte:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Computer science; control theory; systems
Convex and discrete geometry
Exact sciences and technology
F.2.2[Analysis of Algorithms and Problem Complexity]
Geometry
I.3.5[Computational Geometry and Object Modeling]
Isothetic polygon with reflex angles
Line sweep paradigm
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Minimum area polygon
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Optimization problem
Orthoconvex polygon
Polygon enclosing points
Sciences and techniques of general use
Theoretical computing
Computational geometry
Isothetic polygon
Minimum area polygon
Computational complexity
Optimization
Orthoconvex polygon
ISSN:0020-7160, 1029-0265
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Zusammenfassung:We present in this paper, algorithms for finding the minimum area isothetic polygons having two reflex angles containing k points; (k<n) Our algorithms are based on line sweep paradigm. The idea is to enumerate all the polygons in each kind and find the minimum one. We also analyse the complexities of each of the algorithms. We find that out of the four orthogonal polygons with two reflex angles, three are orthoconvex and the algorithms presented for these polygons work in time, where n could be O(n-k) 3 in the worst case. The algorithm for the non-orthoconvex polygon has a complexity of where n could be O((n-k) 3 n) in the worst case.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207160108805081