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Title: Geometric Hitting Set for Segments of Few Orientations

Here 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. Lastly, 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.
Authors:
 [1] ;  [2] ;  [2] ;  [3] ;  [3]
  1. Braunschweig Univ. of Technology (Germany)
  2. Stony Brook Univ., NY (United States)
  3. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Report Number(s):
SAND2016-12946J
Journal ID: ISSN 0302-9743; 650133
Grant/Contract Number:
AC04-94AL85000; 2010074; CCF- 1018388; CCF-1526406
Type:
Accepted Manuscript
Journal Name:
Lecture Notes in Computer Science
Additional Journal Information:
Journal Volume: 9499; Journal ID: ISSN 0302-9743
Publisher:
Springer
Research Org:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING
OSTI Identifier:
1338406

Fekete, Sandor P., Huang, Kan, Mitchell, Joseph S. B., Parekh, Ojas D., and Phillips, Cynthia A.. Geometric Hitting Set for Segments of Few Orientations. United States: N. p., Web. doi:10.1007/978-3-319-28684-6_13.
Fekete, Sandor P., Huang, Kan, Mitchell, Joseph S. B., Parekh, Ojas D., & Phillips, Cynthia A.. Geometric Hitting Set for Segments of Few Orientations. United States. doi:10.1007/978-3-319-28684-6_13.
Fekete, Sandor P., Huang, Kan, Mitchell, Joseph S. B., Parekh, Ojas D., and Phillips, Cynthia A.. 2016. "Geometric Hitting Set for Segments of Few Orientations". United States. doi:10.1007/978-3-319-28684-6_13. https://www.osti.gov/servlets/purl/1338406.
@article{osti_1338406,
title = {Geometric Hitting Set for Segments of Few Orientations},
author = {Fekete, Sandor P. and Huang, Kan and Mitchell, Joseph S. B. and Parekh, Ojas D. and Phillips, Cynthia A.},
abstractNote = {Here 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. Lastly, 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.},
doi = {10.1007/978-3-319-28684-6_13},
journal = {Lecture Notes in Computer Science},
number = ,
volume = 9499,
place = {United States},
year = {2016},
month = {1}
}