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E-approximations for multidimensional weighted location problems.

Z Drezner, B Gavish

    Operations Research
    |June 9, 1985
    PubMed
    Summary
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    This study introduces an efficient algorithm for the multidimensional weighted minimax location problem, minimizing maximal weighted distances. The method provides an epsilon-approximate solution with a time complexity of O(n log epsilon) for fixed dimensions.

    Area of Science:

    • Operations Research
    • Computational Geometry
    • Optimization

    Background:

    • The multidimensional weighted minimax location problem seeks a single facility location to minimize the maximum weighted distance to a set of n demand points.
    • Existing methods may face challenges with high dimensionality and general distance norms.

    Purpose of the Study:

    • To develop an efficient algorithm for the multidimensional weighted minimax location problem.
    • To provide an epsilon-approximate solution using a novel approach.

    Main Methods:

    • A variant of the Russian method for solving Linear Programming problems is adapted.
    • The algorithm is designed to handle general distance norms in a multidimensional space.

    Main Results:

    Related Experiment Videos

    • An epsilon-approximate solution is achieved for the location problem.
    • The algorithm exhibits a time complexity of O(n log epsilon) for a fixed dimensionality k.

    Conclusions:

    • The proposed algorithm offers an efficient approach to the multidimensional weighted minimax location problem.
    • The method's performance is validated through computational results, demonstrating its practical applicability.