k-median问题反向贪心随机算法

Randomized Reverse Greedy Algorithm for k-median Problem

k-median问题的近似算法研究一直是计算机科学工作者关注的焦点。基于均衡限制条件,利用反向贪心策略,给出求解该问题的随机近似算法。证明该算法以较大的概率满足其近似性能比的期望值为(3+O(ln(ln(k)/α))。该算法的时间复杂度为O([kαln(k)]2(n+m)),其中n和m分别代表设施集合以及客户点集的大小。最后,通过计算机实验验证了k-median问题的反向贪心算法的实际计算效果。

Research on the approximated algorithms for k-median problem has been a focus of computer scientists. Based on the balanced parameter, this paper presented a randomized algorithm for k-median problem by means of the re- verse greedy. The new algorithrn＇s expected approximate ratio was proved to be（3 ＋O（ln（ln（k）/a）） with high proba- bility. The running time of the new algorithm is [kin（k）]2 （n＋m）, where n and m represent the nttrnber of clients and facilities for the given instance. Finally, computer verification was used to study the real computational effect of the algorithm.