Information Processing Letters
SCG '86 Proceedings of the second annual symposium on Computational geometry
Art gallery theorems and algorithms
Art gallery theorems and algorithms
Information Processing Letters
Covering grids and orthogonal polygons with periscope guards
Computational Geometry: Theory and Applications
Approximation algorithms for geometric tour and network design problems (extended abstract)
Proceedings of the eleventh annual symposium on Computational geometry
Fast computation of shortest watchman routes in simple polygons
Information Processing Letters
Illumination in the presence of opaque line segments in the plane
Computational Geometry: Theory and Applications
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Touring a sequence of polygons
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Some NP-complete geometric problems
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
Approximation algorithms for TSP with neighborhoods in the plane
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
Cooperative mobile guards in grids
Computational Geometry: Theory and Applications
Guarding a set of line segments in the plane
Theoretical Computer Science
Watchman tours for polygons with holes
Computational Geometry: Theory and Applications
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Given a set $\mathcal L$ of non-parallel lines, a watchman route (tour) for $\mathcal L$ is a closed curve contained in the union of the lines in $\mathcal L$ such that every point on any line is visible (along a line) from at least one point of the route; similarly, we define a watchman route (tour) for a connected set $\mathcal S$ 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 multiply connected polygonal domains. 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. Then, we reprove NP-hardness of this problem for line segments in the plane and provide a polynomial-time approximation algorithm with ratio O(log3n). Additionally, we consider some special cases of the watchman route problem on line segments, for which we provide improved approximation or exact algorithms.