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
The steiner problem with edge lengths 1 and 2,
Information Processing Letters
Covering grids and orthogonal polygons with periscope guards
Computational Geometry: Theory and Applications
A pedestrian approach to ray shooting: shoot a ray, take a walk
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Approximation algorithms for geometric tour and network design problems (extended abstract)
Proceedings of the eleventh annual symposium on Computational geometry
A polylogarithmic approximation algorithm for the group Steiner tree problem
Journal of Algorithms
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
Computing a Shortest Watchman Path in a Simple Polygon in Polynomial-Time
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
Beyond Steiner's Problem: A VLSI Oriented Generalization
WG '89 Proceedings of the 15th International Workshop on Graph-Theoretic Concepts in Computer Science
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
A tight bound on approximating arbitrary metrics by tree metrics
Journal of Computer and System Sciences - Special issue: STOC 2003
Cooperative mobile guards in grids
Computational Geometry: Theory and Applications
Optimal dynamic vertical ray shooting in rectilinear planar subdivisions
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Coverage with k-transmitters in the presence of obstacles
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
Guarding a set of line segments in the plane
Theoretical Computer Science
Watchman tours for polygons with holes
Computational Geometry: Theory and Applications
Complexity of minimum corridor guarding problems
Information Processing Letters
Minimization of the maximum distance between the two guards patrolling a polygonal region
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
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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.