Computing optimal islands

Authors:
C. Bautista-Santiago;J. M. DíAz-BáñEz;D. Lara;P. PéRez-Lantero;J. Urrutia;I. Ventura
Affiliations:
Universidad Nacional Autónoma de México, Mexico;Departamento Matemática Aplicada II. Escuela Técnica Superior de Ingenieros. Camino de los Descubrimientos, s/n, 41092, Sevilla, Spain;Universidad Nacional Autónoma de México, Mexico;Universidad de Valparaiso, Chile;Universidad Nacional Autónoma de México, Mexico;Universidad de Sevilla, Spain
Venue:
Operations Research Letters
Year:
2011

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Abstract

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(logn)-approximation for the problem of computing the minimum number of convex polygons that cover a class region.