Constrained Minimum Enclosing Circle with Center on a Query Line Segment
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(log2 n). We will use this method for solving the following problem proposed by Bose and Wang  – 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+mlog2 n) time using our method in a much simpler way than ; the time complexity of the problem is also being improved.
KeywordsIntersection Point Leaf Node Space Complexity Voronoi Diagram Convex Polygon
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