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Theory of Computing Systems

, Volume 62, Issue 2, pp 268–303 | Cite as

Geometric Hitting Set for Segments of Few Orientations

  • Sándor P. Fekete
  • Kan Huang
  • Joseph S. B. Mitchell
  • Ojas Parekh
  • Cynthia A. Phillips
Article
  • 160 Downloads

Abstract

We study several natural instances of the geometric hitting set problem for input consisting of sets of line segments (and rays, lines) having a small number of distinct slopes. These problems model path monitoring (e.g., on road networks) using the fewest sensors (the “hitting points”). We give approximation algorithms for cases including (i) lines of 3 slopes in the plane, (ii) vertical lines and horizontal segments, (iii) pairs of horizontal/vertical segments. We give hardness and hardness of approximation results for these problems. We prove that the hitting set problem for vertical lines and horizontal rays is polynomially solvable.

Keywords

Set cover Hitting set Approximation algorithms 

Notes

Acknowledgments

This work is supported by the Laboratory Directed Research and Development program at Sandia National Laboratories, a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000. J. Mitchell acknowledges support from the US-Israel Binational Science Foundation (grant 2010074) and the National Science Foundation (CCF-1018388, CCF-1526406).

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.TU BraunschweigBraunschweigGermany
  2. 2.Stony Brook UniversityStony BrookUSA
  3. 3.Sandia National LabsAlbuquerqueUSA

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