Abstract
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.
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The first and the third author were supported in part by the National Science Foundation under Grants CCR-9623585 and CCR-9988468. The second author was supported in part by the National Science Foundation under Grants MIP-9701416 and CCR-9988468, and by HP Labs, Bristol, England, under an external research program grant.
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Chen, D.Z., Hu, X., Wu, X. (2000). Optimal Polygon Cover Problems and Applications. In: Goos, G., Hartmanis, J., van Leeuwen, J., Lee, D.T., Teng, SH. (eds) Algorithms and Computation. ISAAC 2000. Lecture Notes in Computer Science, vol 1969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40996-3_48
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DOI: https://doi.org/10.1007/3-540-40996-3_48
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