An Efficient Local Search Algorithm for k-Median Problem

The k-median problem is one of the NP-hard combinatorial optimization problems. It falls into the general class of clustering problem and has application in the field of classification and data mining. One has confirmed that local search technique is the most effective and simplest method for designing the algorithms for k-median problem, and has been looking for the more efficient algorithms which can simplify the search space of the problem to solve the large-scale instance and obtain the high quality solution. In this paper, we first analyze the search space of the problem by making use of fitness distance correlation method and reveal the relation between local minima and global minima, and then we propose a more effective and efficient algorithm which gradually scales down the size of the instance based on the intersection of local minima so that the original search space is simplified and the better solution is found. Finally, elaborate experimental results attest the efficiency and computational effect of the algorithm. Key–Words: k-Median, NP-hard, Combinatorial optimization, Local search, Approximation algorithm