Abstract
Let P be a convex polygon with n vertices. We want to find two congruent disks whose union covers P and whose radius is minimized. We also consider its discrete version with centers restricted to be at vertices of P. Standard and discrete two-center problems are respectively solved in O(n log3 n log log n) and O(n log2 n) time. Furthermore, we can solve both of the standard and discrete two-center problems for a set of points in convex positions in O(nlog2 n) time.
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Kim, S.K., Shin, CS. (2000). Efficient Algorithms for Two-Center Problems for a Convex Polygon. In: Du, DZ., Eades, P., Estivill-Castro, V., Lin, X., Sharma, A. (eds) Computing and Combinatorics. COCOON 2000. Lecture Notes in Computer Science, vol 1858. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44968-X_30
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DOI: https://doi.org/10.1007/3-540-44968-X_30
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