Abstract
Given a set P of n points and a straight line L, we study three important variations of minimum enclosing circle problem. The first problem is on computing k circles of minimum (common) radius with centers on L which can cover the members in P. We propose three algorithms for this problem. The first one runs in O(nklogn) time and O(n) space. The second one runs in O(nk + k 2log3 n) time and O(nlogn) space assuming that the points are sorted along L, and is efficient where k < < n. The third one is based on parametric search and it runs in O(nlogn + klog4 n) time. The next one is on computing the minimum radius circle centered on L that can enclose at least k points. The time and space complexities of the proposed algorithm are O(nk) and O(n) respectively. Finally, we study the situation where the points are associated with k colors, and the objective is to find a minimum radius circle with center on L such that at least one point of each color lies inside it. We propose an O(nlogn) time algorithm for this problem.
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Karmakar, A., Das, S., Nandy, S.C., Bhattacharya, B.K. (2010). Some Variations on Constrained Minimum Enclosing Circle Problem. In: Wu, W., Daescu, O. (eds) Combinatorial Optimization and Applications. COCOA 2010. Lecture Notes in Computer Science, vol 6508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17458-2_29
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