Computational geometry: an introduction
Computational geometry: an introduction
Triangulating a simple polygon in linear time
Discrete & Computational Geometry
An output-sensitive algorithm for computing visibility
SIAM Journal on Computing
Optimizing the sum of linear fractional functions
Recent advances in global optimization
Computing minimum length paths of a given homotopy class
Computational Geometry: Theory and Applications
On some geometric optimization problems in layered manufacturing
Computational Geometry: Theory and Applications
Computing the arrangement of curve segments: divide-and-conquer algorithms via sampling
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Optimizing the sum of linear fractional functions and applications
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Robotic Radiosurgery with Beams of Adaptable Shapes
CVRMed '95 Proceedings of the First International Conference on Computer Vision, Virtual Reality and Robotics in Medicine
Optimal Terrain Construction Problems and Applications in Intensity-Modulated Radiation Therapy
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
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Polygon cover problems arise in computational geometry and in a number of applied areas, such as material layout, layered manufacturing, radiation therapy and radiosurgery, etc. In this paper, we study three optimal polygon cover problems: monotone polygon cover with obstacles, star-shaped polygon cover with obstacles, and rectangular cover. Based on useful geometric observations, we develop efficient algorithms for solving these problems. Either our algorithms improve the quality of the previously best known solutions for these polygon cover problems, or our complexity bounds are comparable to those of the previously best known algorithms for simpler cases of the problems.