On-line construction of the convex hull of a simple polyline
Information Processing Letters
Information Processing Letters
Information Processing Letters
Shortest watchman routes in simple polygons
Discrete & Computational Geometry
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Watchman routes under limited visibility
Computational Geometry: Theory and Applications
Minimal link visibility paths inside a simple polygon
Computational Geometry: Theory and Applications
Finding an approximate minimum-link visibility path inside a simple polygon
Information Processing Letters
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
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
Constructing Shortest Watchman Routes by Divide-and-Conquer
ISAAC '93 Proceedings of the 4th International Symposium on Algorithms and Computation
Concerning the Time Bounds of Existing Shortest Watchman Route Algorithms
FCT '97 Proceedings of the 11th International Symposium on Fundamentals of Computation Theory
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)
Linear-Time 2-approximation algorithm for the watchman route problem
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Approximate solution of the multiple watchman routes problem with restricted visibility range
IEEE Transactions on Neural Networks
A Sensor Placement Algorithm for a Mobile Robot Inspection Planning
Journal of Intelligent and Robotic Systems
Visiting convex regions in a polygonal map
Robotics and Autonomous Systems
A survey on coverage path planning for robotics
Robotics and Autonomous Systems
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The watchman route problem (WRP) was first introduced in 1988 and is defined as follows: How to calculate a shortest route completely contained inside a simple polygon such that any point inside this polygon is visible from at least one point on the route? So far the best known result for the WRP is an O(n3log n) runtime algorithm (with inherent numerical problems of its implementation). This paper gives an κ(Ɛ) × O(kn) approximate algorithm for WRP by using a rubberband algorithm, where n is the number of vertices of the simple polygon, k the number of essential cuts, Ɛ the chosen accuracy constant for the minimization of the calculated route, and κ(Ɛ) equals the length of the initial route minus the length of the calculated route, divided by Ɛ.