Visibility and intersection problems in plane geometry
Discrete & Computational Geometry
Computational geometry in C
Finding an approximate minimum-link visibility path inside a simple polygon
Information Processing Letters
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
Fast computation of shortest watchman routes in simple polygons
Information Processing Letters
Touring a sequence of polygons
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Approximation algorithms for the watchman route and zookeeper's problems
Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
An approximate algorithm for solving the watchman route problem
RobVis'08 Proceedings of the 2nd international conference on Robot vision
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Given a simple polygon P of n vertices, the watchman route problem asks for a shortest (closed) route inside P such that each point in the interior of P can be seen from at least one point along the route. We present a simple, linear-time algorithm for computing a watchman route of length at most 2 times that of the shortest watchman route. The best known algorithm for computing a shortest watchman route takes O(n4 log n) time, which is too complicated to be suitable in practice. This paper also involves an optimal O(n) time algorithm for computing the set of so-called essential cuts, which are the line segments inside the polygon P such that any route visiting them is a watchman route. It solves an intriguing open problem by improving the previous O(n log n) time result, and is thus of interest in its own right.