Covering a Set of Points with a Minimum Number of Lines

  • Magdalene Grantson
  • Christos Levcopoulos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3998)

Abstract

We consider the minimum line covering problem: given a set S of n points in the plane, we want to find the smallest number l of straight lines needed to cover all n points in S. We show that this problem can be solved in O(n log l) time if lO(log1 − εn), and that this is optimal in the algebraic computation tree model (we show that the Ω(nlog l) lower bound holds for all values of l up to \(O(\sqrt n)\)). Furthermore, a O(log l)-factor approximation can be found within the same O(n log l) time bound if \(l \in O(\sqrt[4]{n})\). For the case when l ∈ Ω(log n) we suggest how to improve the time complexity of the exact algorithm by a factor exponential in l.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Magdalene Grantson
    • 1
  • Christos Levcopoulos
    • 1
  1. 1.Department of Computer ScienceLund UniversityLundSweden

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