Biogeometry Coresets for Shape Fitting and Kinetic Data Structures
نویسندگان
چکیده
Background. Computing various descriptors of the extent of a set P of n points in Rd has found many useful applications in shape analysis, data mining and other areas. These descriptors, called extent measures, either compute statistics of P itself (e.g., diameter, width), or they compute statistics of a (possibly nonconvex) geometric shape (e.g., sphere, box, cylindrical shell) enclosing P. Although traditionally P is assumed to be stationary, some recent applications, including the protein-structure analysis, call for maintaining extent measures of a set of moving points. These points may represent a rigid body in motion or a deformable object. The exact algorithms for computing most of these extent measures are generally expensive, and faster approximation algorithms are more suitable for these problems.
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