A deterministic algorithm for fitting a step function to a weighted point-set
Type
ArticleKAUST Department
Visual Computing Center (VCC)Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Computer Science Program
Geometric Algorithms Group
Date
2013-02Preprint Posting Date
2011-09-06Permanent link to this record
http://hdl.handle.net/10754/562621
Metadata
Show full item recordAbstract
Given a set of n points in the plane, each point having a positive weight, and an integer k>0, we present an optimal O(nlogn)-time deterministic algorithm to compute a step function with k steps that minimizes the maximum weighted vertical distance to the input points. It matches the expected time bound of the best known randomized algorithm for this problem. Our approach relies on Coles improved parametric searching technique. As a direct application, our result yields the first O(nlogn)-time algorithm for computing a k-center of a set of n weighted points on the real line. © 2012 Elsevier B.V.Publisher
Elsevier BVJournal
Information Processing LettersarXiv
arXiv:1109.1152Additional Links
http://arxiv.org/abs/arXiv:1109.1152v2ae974a485f413a2113503eed53cd6c53
10.1016/j.ipl.2012.11.003