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Theory of Computing Systems

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06-02-2017

Geometric Hitting Set for Segments of Few Orientations

Authors: Sándor P. Fekete, Kan Huang, Joseph S. B. Mitchell, Ojas Parekh, Cynthia A. Phillips

Published in: Theory of Computing Systems | Issue 2/2018

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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.

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Title: Geometric Hitting Set for Segments of Few Orientations
Authors: Sándor P. Fekete
Kan Huang
Joseph S. B. Mitchell
Ojas Parekh
Cynthia A. Phillips
Publication date: 06-02-2017
Publisher: Springer US
Published in: Theory of Computing Systems / Issue 2/2018
Print ISSN: 1432-4350
Electronic ISSN: 1433-0490
DOI: https://doi.org/10.1007/s00224-016-9744-7

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