Fast Computation of Smallest Enclosing Circle with Center on a Query Line Segment

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 = {p1, p2, . . . , pn} 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. [11] has proposed an algorithm for this problem that reports the location of the center of the smallest enclosing circle C ′ on a query line segment in O(log n) time. Our algorithm improves the query time compared to [11]. The reporting time for this problem is O(log n) and both the preprocessing time and space complexities are O(n).