A linear-time algorithm for computing the Voronoi diagram of a convex polygon
Discrete & Computational Geometry
Facility Location Constrained to a Polygonal Domain
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
SFCS '75 Proceedings of the 16th Annual Symposium on Foundations of Computer Science
Farthest-point queries with geometric and combinatorial constraints
Computational Geometry: Theory and Applications
Fast computation of smallest enclosing circle with center on a query line segment
Information Processing Letters
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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In this paper, we will study the problem of locating the center of smallest enclosing circle of a set P of n points, where the center is constrained to lie on a query line segment. The preprocessing time and space complexities of our proposed algorithm are O(n logn) and O(n) respectively; the query time complexity is O(log2n). We will use this method for solving the following problem proposed by Bose and Wang [3] – given r simple polygons with a total of m vertices along with the point set P, compute the smallest enclosing circle of P whose center lies in one of the r polygons. This can be solved in O( nlogn+mlog2n) time using our method in a much simpler way than [3]; the time complexity of the problem is also being improved.