Practical Methods for Shape Fitting and Kinetic Data Structures using Coresets

The notion of -kernel was introduced by Agarwal et al. [5] to set up a unified framework for computing various extent measures of a point set P approximately. Roughly speaking, a subset Q P is an -kernel of P if for every slab W containing Q, the expanded slab (1 + )W contains P. They illustrated the significance of -kernel by showing that it yields approximation algorithms for a wide range of geometric optimization problems. We present a simpler and more practical algorithm for computing the -kernel of a set P of points in Rd . We demonstrate the practicality of our algorithm by showing its empirical performance on various inputs. We then describe an incremental algorithm for fitting various shapes and use the ideas of our algorithm for computing -kernels to analyze the performance of this algorithm. We illustrate the versatility and practicality of this technique by implementing approximation algorithms for minimum enclosing cylinder, minimum-volume bounding box, and minimum-width ...

• Type: Journal
• Year: 2008
• Where: ALGORITHMICA
• Authors: Hai Yu, Pankaj K. Agarwal, Raghunath Poreddy, Kasturi R. Varadarajan
• Keywords: Agarwal Et Al, ALGORITHMICA 2008, Algorithms, Approximation Algorithms