International Workshop on Approximation and Online Algorithms

Approximation and Online Algorithms pp 145-157

Geometric Hitting Set for Segments of Few Orientations

  • Sándor P. Fekete
  • Kan Huang
  • Joseph S. B. Mitchell
  • Ojas Parekh
  • Cynthia A. Phillips
Conference paper

DOI: 10.1007/978-3-319-28684-6_13

Volume 9499 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Fekete S.P., Huang K., Mitchell J.S.B., Parekh O., Phillips C.A. (2015) Geometric Hitting Set for Segments of Few Orientations. In: Sanità L., Skutella M. (eds) Approximation and Online Algorithms. Lecture Notes in Computer Science, vol 9499. Springer, Cham

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.

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Sándor P. Fekete
    • 1
  • Kan Huang
    • 2
  • Joseph S. B. Mitchell
    • 2
  • Ojas Parekh
    • 3
  • Cynthia A. Phillips
    • 3
  1. 1.TU BraunschweigBraunschweigGermany
  2. 2.Stony Brook UniversityStony BrookUSA
  3. 3.Sandia National LabsAlbuquerqueUSA