Approximation algorithms for k-line center


Conference Paper

© Springer-Verlag Berlin Heidelberg 2002. Given a set P of n points in Rd and an integer k ≥ 1, let w* denote the minimum value so that P can be covered by k cylinders of radius at most (1 + ε )w*. We describe an algorithm that, given P and an ε> 0, computes k cylinders of radius at most (1 + ε)w* that cover P. The running time of the algorithm is O(n log n), with the constant of proportionality depending on k, d, and e. We first show that there exists a small "certificate" Q #x2286; P, whose size does not depend on n, such that for any k-cylinders that cover Q, an expansion of these cylinders by afactorof(1 + ε)covers P. We then use a well-known scheme based on sampling and iterated re-weighting for computing the cylinders.

Full Text

Duke Authors

Cited Authors

  • Agarwal, PK; Procopiuc, CM; Varadarajan, KR

Published Date

  • January 1, 2002

Published In

Volume / Issue

  • 2461 /

Start / End Page

  • 54 - 63

Electronic International Standard Serial Number (EISSN)

  • 1611-3349

International Standard Serial Number (ISSN)

  • 0302-9743

International Standard Book Number 10 (ISBN-10)

  • 3540441808

International Standard Book Number 13 (ISBN-13)

  • 9783540441809

Digital Object Identifier (DOI)

  • 10.1007/3-540-45749-6_9

Citation Source

  • Scopus