A constant-factor approximation algorithm for the k-median problem (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Local search heuristic for k-median and facility location problems
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A Taxonomy of Hybrid Metaheuristics
Journal of Heuristics
New Genetic Local Search Operators for the Traveling Salesman Problem
PPSN IV Proceedings of the 4th International Conference on Parallel Problem Solving from Nature
Improved Combinatorial Algorithms for the Facility Location and k-Median Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Primal-Dual Approximation Algorithms for Metric Facility Location and k-Median Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Solving traveling salesman problems by combining global and local search mechanisms
CEC '02 Proceedings of the Evolutionary Computation on 2002. CEC '02. Proceedings of the 2002 Congress - Volume 02
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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.