ε-Approximations for Multidimensional Weighted Location Problems

This paper considers the multidimensional weighted minimax location problem, namely, finding a facility location that minimizes the maximal weighted distance to n points. General distance norms are used. An ε-approximate solution is obtained by applying a variant of the Russian method for the solution of Linear Programming. The algorithm has a time complexity of O(n log ε) for fixed dimensionality k. Computational results are presented.