A space-optimal data-stream algorithm for coresets in the plane

Given a point set P R2 , a subset Q P is an -kernel of P if for every slab W containing Q, the (1+)-expansion of W also contains P. We present a data-stream algorithm for maintaining an -kernel of a stream of points in R2 that uses O(1/ ) space and takes O(log(1/)) amortized time to process each point. This is the first space-optimal data-stream algorithm for this problem. As a consequence, we obtain improved data-stream approximation algorithms for other extent measures, such as width, robust kernels, as well as -kernels in higher dimensions.

• Type: Conference
• Year: 2007
• Where: COMPGEOM
• Authors: Pankaj K. Agarwal, Hai Yu
• Keywords: COMPGEOM 2007, Data-stream Algorithm, Data-stream Approximation Algorithms, Discrete Geometry, Space-optimal Data-stream Algorithm