Computational geometry: an introduction
Computational geometry: an introduction
Optimal point location in a monotone subdivision
SIAM Journal on Computing
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Facility Location Constrained to a Polygonal Domain
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Computing the Constrained Euclidean Geodesic and Link Center of a Simple Polygon with Applications
CGI '96 Proceedings of the 1996 Conference on Computer Graphics International
SFCS '75 Proceedings of the 16th Annual Symposium on Foundations of Computer Science
Constrained minimum enclosing circle with center on a query line segment
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Some variations on constrained minimum enclosing circle problem
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Some variations on constrained minimum enclosing circle problem
Journal of Combinatorial Optimization
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Here we propose an efficient algorithm for computing the smallest enclosing circle whose center is constrained to lie on a query line segment. Our algorithm preprocesses a given set of n points P={p"1,p"2,...,p"n} such that for any query line or line segment L, it efficiently locates a point c on L that minimizes the maximum distance among the points in P from c. Roy et al. [S. Roy, A. Karmakar, S. Das, S.C. Nandy, Constrained minimum enclosing circle with center on a query line segment, in: Proc. of the 31st Mathematical Foundation of Computer Science, 2006, pp. 765-776] have proposed an algorithm that solves the query problem in O(log^2n) time using O(nlogn) preprocessing time and O(n) space. Our algorithm improves the query time to O(logn); but the preprocessing time and space complexities are both O(n^2).