article

Watchman routes for lines and line segments

Authors:

Adrian Dumitrescu,

Joseph S. B. Mitchell,

Paweł ŻylińskiAuthors Info & Claims

Computational Geometry: Theory and Applications, Volume 47, Issue 4

Pages 527 - 538

https://doi.org/10.1016/j.comgeo.2013.11.008

Published: 01 May 2014 Publication History

Abstract

Given a set L of non-parallel lines in the plane, a watchman route (tour) for L is a closed curve contained in the union of the lines in L such that every line is visited (intersected) by the route; we similarly define a watchman route (tour) for a connected set S of line segments. The watchman route problem for a given set of lines or line segments is to find a shortest watchman route for the input set, and these problems are natural special cases of the watchman route problem in a polygon with holes (a polygonal domain). In this paper, we show that the problem of computing a shortest watchman route for a set of n non-parallel lines in the plane is polynomially tractable, while it becomes NP-hard in 3D. We give an alternative NP-hardness proof of this problem for line segments in the plane and obtain a polynomial-time approximation algorithm with ratio O(log^3n). Additionally, we consider some special cases of the watchman route problem on line segments, for which we provide exact algorithms or improved approximations.

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Cited By

Wang THuang PDong GZhao Y(2023)A Diffusion-Based Reactive Approach to Road Network Cooperative Persistent SurveillanceIEEE Transactions on Intelligent Transportation Systems10.1109/TITS.2023.332900125:5(4265-4277)Online publication date: 21-Nov-2023
https://dl.acm.org/doi/10.1109/TITS.2023.3329001
Li Q(2020)Visionbased Sensor Coverage in Uncertain Geometric DomainsACM SIGMETRICS Performance Evaluation Review10.1145/3380908.338091447:3(17-19)Online publication date: 23-Jan-2020
https://dl.acm.org/doi/10.1145/3380908.3380914
Dereniowski DOno HSuzuki IWrona ŁYamashita MŻyliński P(2019)The searchlight problem for road networksTheoretical Computer Science10.1016/j.tcs.2015.04.026591:C(28-59)Online publication date: 6-Jan-2019
https://dl.acm.org/doi/10.1016/j.tcs.2015.04.026

Watchman routes for lines and line segments

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cover image Computational Geometry: Theory and Applications

Computational Geometry: Theory and Applications Volume 47, Issue 4

May, 2014

36 pages

ISSN:0925-7721

Issue’s Table of Contents

Copyright © Elsevier B.V. © 2013.

Publisher

Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 May 2014

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Cited By

Wang THuang PDong GZhao Y(2023)A Diffusion-Based Reactive Approach to Road Network Cooperative Persistent SurveillanceIEEE Transactions on Intelligent Transportation Systems10.1109/TITS.2023.332900125:5(4265-4277)Online publication date: 21-Nov-2023
https://dl.acm.org/doi/10.1109/TITS.2023.3329001
Li Q(2020)Visionbased Sensor Coverage in Uncertain Geometric DomainsACM SIGMETRICS Performance Evaluation Review10.1145/3380908.338091447:3(17-19)Online publication date: 23-Jan-2020
https://dl.acm.org/doi/10.1145/3380908.3380914
Dereniowski DOno HSuzuki IWrona ŁYamashita MŻyliński P(2019)The searchlight problem for road networksTheoretical Computer Science10.1016/j.tcs.2015.04.026591:C(28-59)Online publication date: 6-Jan-2019
https://dl.acm.org/doi/10.1016/j.tcs.2015.04.026

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