Abstract: In this paper two kinds of algorithms for solving the k（＜n） center problem are proposed Here the first kind of algorithm is fit for the case k ＜10, whereas the second one is fit for the case 10＜ k＜n The ideas of the two kinds of algorithms are different The former uses a method which aliquots the diameter of a convex hull and the center position of the circle determined by it is fixed, but the latter adopts a method in which multi parameters are randomized, thus keeping the center of the circle indeterminate Moreover the correctness of the two algorithms is also proved and their time complexity is analyzed