Efficient Speed-Up of the Smallest Enclosing Circle Algorithm

Solution Methodologies for the Smallest Enclosing Circle Problem

Given a set of circles C = {c1, ..., cn} on the Euclidean plane with centers {(a1, b1), ..., (an, bn)} and radii {r1, ..., rn}, the smallest enclosing circle (of fixed circles ) problem is to find the circle of minimum radius that encloses all circles in C. We survey four known approaches for this problem, including a second order cone reformulation, a subgradient approach, a quadratic programm...

Computing the Smallest k-Enclosing Circle and Related Problems

We present an e cient algorithm for solving the \smallest k-enclosing circle" ( kSC ) problem: Given a set of n points in the plane and an integer k n, nd the smallest disk containing k of the points. We present two solutions. When using O(nk) storage, the problem can be solved in time O(nk log 2 n). When only O(n logn) storage is allowed, the running time is O(nk log 2 n log n k ). This proble...

Smallest enclosing circle centered on a query line segment

Given a set of n points P = {p1, p2, . . . , pn} in the plane, we show how to preprocess P such that for any query line segment L we can report in O(log n) time the smallest enclosing circle whose center is constrained to lie on L . The preprocessing time and space complexity are O(n log n) and O(n) respectively. We then show how to use this data structure in order to compute the smallest enclo...

Efficient Algorithms for the Smallest Enclosing Ball Problem

Consider the problem of computing the smallest enclosing ball of a set of m balls in 30. In this paper we develop two algorithms that are particularly suitable for problems where n is large. The first algorithm is based on log-exponential aggregation of the maximum function and reduces the problem into an unconstrained convex program....

Efficient Algorithms for the Smallest Enclosing Cylinder Problem