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The max-sum inverse median location problem on trees with budget constraint

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  • Nguyen-Thu, Huong
  • Nguyen, Kien Trung
  • Toan, Nguyen Thanh

Abstract

The theory of inverse location involves modifying parameters in such a way that the total cost is minimized and one/several prespecified facilities become optimal based on these perturbed parameters. When the modifying parameters are grouped into sets, with each group's cost measured under the rectilinear norm and the overall cost measured under the Chebyshev norm, the resulting problem is known as the max-sum inverse location problem. This paper addresses the max-sum inverse median location problem on trees with a budget constraint, where the objective is to modify the vertex weights so that a specified vertex becomes a 1-median, while minimizing the max-sum objective within the available budget. To solve this problem, a uni-variable optimization problem is first induced, where the objective function for each specified value of the variable can be obtained through a continuous knapsack problem. Leveraging the monotonicity of the cost function, a combinatorial algorithm is developed, which solves the problem in O(nlog⁡n) time, where n denotes the number of vertices present in the tree.

Suggested Citation

  • Nguyen-Thu, Huong & Nguyen, Kien Trung & Toan, Nguyen Thanh, 2024. "The max-sum inverse median location problem on trees with budget constraint," Applied Mathematics and Computation, Elsevier, vol. 460(C).
    • Handle: RePEc:eee:apmaco:v:460:y:2024:i:c:s0096300323004654
    DOI: 10.1016/j.amc.2023.128296
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    References listed on IDEAS

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    1. Kien Trung Nguyen, 2016. "Inverse 1-Median Problem on Block Graphs with Variable Vertex Weights," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 944-957, March.
    2. Behrooz Alizadeh & Esmaeil Afrashteh & Fahimeh Baroughi, 2018. "Combinatorial Algorithms for Some Variants of Inverse Obnoxious Median Location Problem on Tree Networks," Journal of Optimization Theory and Applications, Springer, vol. 178(3), pages 914-934, September.
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