Covering Paths for Planar Point Sets

  • Adrian Dumitrescu
  • Csaba D. Tóth
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7704)

Abstract

Given a set of points, a covering path is a directed polygonal path that visits all the points. We show that for any n points in the plane, there exists a (possibly self-crossing) covering path consisting of n/2 + O(n/logn) straight line segments. If no three points are collinear, any covering path (self-crossing or non-crossing) needs at least n/2 segments. If the path is required to be non-crossing, n − 1 straight line segments obviously suffice and we exhibit n-element point sets which require at least 5n/9 − O(1) segments in any such path. Further, we show that computing a non-crossing covering path for n points in the plane requires Ω(n logn) time in the worst case.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Adrian Dumitrescu
    • 1
  • Csaba D. Tóth
    • 2
  1. 1.Computer ScienceUniversity of Wisconsin–MilwaukeeUSA
  2. 2.Mathematics and StatisticsUniversity of CalgaryCanada

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