Algorithms for two-box covering

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Algorithms for two-box covering
We study the problem of covering a set of points or polyhedra in 3 with two axis-aligned boxes in order to minimize a function of the measures of the two boxes, such as the sum or the maximum of their volumes. This 2-box cover problem arises naturally in the construction of bounding volume hierarchies, as well as in shape approximation and clustering. Existing algorithms solve the min-max version of the exact problem in quadratic time. Our results are more general, addressing min-max, min-sum and other versions. Our results give the first approximation schemes for the problem, which run in nearly linear time, as well as some new exact algorithms. We give (1 + ε)-approximation algorithms for minimizing the maximum or sum of volumes (or surface areas, diameters, widths, or girths) of the two boxes in 3 . We investigate also the problem of computing balanced coverings, in which each box covers at least a fraction of the input objects, and we discuss the application to constructing prov...
Esther M. Arkin, Gill Barequet, Joseph S. B. Mitch
Added 13 Jun 2010
Updated 13 Jun 2010
Type Conference
Year 2006
Authors Esther M. Arkin, Gill Barequet, Joseph S. B. Mitchell
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