Computing optimal islands

Computing optimal islands

Let S be a bicolored set of n points in the plane. A subset I of S is an island if there is a convex set C such that I = C ∩ S . We give an O ( n 3 ) -time algorithm to compute a monochromatic island of maximum cardinality. Our approach is adapted to optimize similar (decomposable) objective functio...

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Veröffentlicht in:Operations research letters 2011-07, Vol.39 (4), p.246-251
Hauptverfasser: Bautista-Santiago, C., Díaz-Báñez, J.M., Lara, D., Pérez-Lantero, P., Urrutia, J., Ventura, I.
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Applied sciences
Classification
Computation
Computational geometry
Exact sciences and technology
Islands
Mathematical analysis
Mathematical models
Mathematical programming
Maximum convex polygon
Operational research and scientific management
Operational research. Management science
Operations research
Optimization
Polygons
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Beschreibung
Zusammenfassung:Let S be a bicolored set of n points in the plane. A subset I of S is an island if there is a convex set C such that I = C ∩ S . We give an O ( n 3 ) -time algorithm to compute a monochromatic island of maximum cardinality. Our approach is adapted to optimize similar (decomposable) objective functions. Finally, we use our algorithm to give an O ( log n ) -approximation for the problem of computing the minimum number of convex polygons that cover a class region.
ISSN:0167-6377
1872-7468
DOI:10.1016/j.orl.2011.04.008