approach in linear time when dimension is fixed. In 1991, Emo Welzl proposed a much simpler randomized algorithm based in the extension of a randomized linear programming algorithm by Raimund Seidel. It runs in expected linear time. The paper provides experimental results demonstrating its practicality in higher dimensions. The open-source Computational Geometry Algorithms Library (CGAL) contains an implementation of this algorithm. Ritter's bounding sphere In 1990, Jack Ritter proposed a simple algorithm to find a non-minimal bounding sphere. It is widely used in various applications for its simplicity. The algorithm works in this way: Pick a point from , search a point in , which has the largest distance from ; Search a point in , which has the largest distance from . Set up an initial ball , with its centre as the midpoint of and , the radius as half of the distance between and ; If all points in are within ball , then we get a bounding sphere. Otherwise, let be a point outside the ball, construct a new ball covering both point and previous ball. Repeat this step until all points are covered. Ritter's algorithm runs in time on inputs consisting of points in -dimensional space, which makes it very efficient. However it gives only a coarse result which is usually 5% to 20% larger than the optimum. Core-set based approximation Bădoiu et al. presented a approximation to the bounding sphere problem, where a approximation means that the constructed sphere has radius at most , where is the smallest possible radius of a bounding sphere. A coreset is a small subset, that a expansion of the solution on the subset is a bounding sphere of the whole set. The coreset is constructed incrementally by adding the farthest point into the set in each iteration. Kumar et al. improved this approximation algorithm so that it runs in time . Fischer's exact solver Fischer et al. (2003) proposed an exact solver, though the algorithm does not have a polynomial running time in the worst case. The algorithm is purely combinatorial and implements a pivoting scheme similar to the simplex method for linear programming, used earlier in some heuristics. It starts with a large sphere that covers all points and gradually shrinks it until it cannot be shrunk further. The algorithm features correct termination rules in cases of degeneracies, overlooked by prior authors; and efficient handling of partial