# Geometric Hitting Set for Segments of Few Orientations

Geometric Hitting Set for Segments of Few Orientations 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Theory of Computing Systems Springer Journals

# Geometric Hitting Set for Segments of Few Orientations

Theory of Computing Systems, Volume 62 (2) – Feb 6, 2017
36 pages

/lp/springer_journal/geometric-hitting-set-for-segments-of-few-orientations-4rgE2KFEGG
Publisher
Springer Journals
Subject
Computer Science; Theory of Computation
ISSN
1432-4350
eISSN
1433-0490
D.O.I.
10.1007/s00224-016-9744-7
Publisher site
See Article on Publisher Site

### 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.

### Journal

Theory of Computing SystemsSpringer Journals

Published: Feb 6, 2017

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