Geometric Hitting Set for Segments of Few Orientations

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

doi:10.1007/s00224-016-9744-7

Title: Geometric Hitting Set for Segments of Few Orientations

Journal Article · Mon Feb 06 00:00:00 EST 2017 · Theory of Computing Systems

DOI:https://doi.org/10.1007/s00224-016-9744-7· OSTI ID:1464175

Fekete, Sándor P. ^[1]; Huang, Kan ^[2];

^[2]; Parekh, Ojas ^[3]; Phillips, Cynthia A. ^[3]

Braunschweig Univ. of Technology (Germany)
Stony Brook Univ., NY (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

In this paper, 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. Finally, we prove that the hitting set problem for vertical lines and horizontal rays is polynomially solvable.

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Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Stony Brook Univ., NY (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); SNL Laboratory Directed Research and Development (LDRD) Program; US-Israel Binational Science Foundation; National Science Foundation (NSF)

Grant/Contract Number:: AC04-94AL85000; 2010074; CCF-1018388; CCF-1526406

OSTI ID:: 1464175

Report Number(s):: SAND-2016-12946J; 650133

Journal Information:: Theory of Computing Systems, Vol. 62, Issue 2; ISSN 1432-4350

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 3 works

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Graphs with equal domination and covering numbers Lingas, Andrzej; Miotk, Mateusz; Topp, Jerzy Journal of Combinatorial Optimization, Vol. 39, Issue 1 https://doi.org/10.1007/s10878-019-00454-6	journal	October 2019
Graphs with equal domination and covering numbers Lingas, Andrzej; Miotk, Mateusz; Topp, Jerzy arXiv https://doi.org/10.48550/arxiv.1802.09051	text	January 2018

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