An Almost Space-Optimal Streaming Algorithm for Coresets in Fixed Dimensions

We present a new streaming algorithm for maintaining an -kernel of a point set in Rd using O((1/(d-1)/2 ) log(1/)) space. The space used by our algorithm is optimal up to a small logarithmic factor. This substantially improves (for any fixed dimension d 3) the best previous algorithm for this problem that uses O(1/d-(3/2) ) space, presented by Agarwal and Yu at SoCG'07. Our algorithm immediately improves the space complexity of the best previous streaming algorithms for a number of fundamental geometric optimization problems in fixed dimensions, including width, minimum enclosing cylinder, minimum-width enclosing annulus, minimum-width enclosing cylindrical shell, etc.

• Type: Conference
• Year: 2008
• Where: ESA
• Authors: Hamid Zarrabi-Zadeh
• Keywords: Algorithms, ESA 2008, Fixed Dimensions, Minimum Enclosing Cylinder, Streaming Algorithms