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A linear time algorithm for the p-maxian problem on trees with distance constraint

Author

Listed:
  • Trung Kien Nguyen

    (Teacher College, Can Tho University)

  • Nguyen Thanh Hung

    (Teacher College, Can Tho University)

  • Huong Nguyen-Thu

    (Teacher College, Can Tho University)

Abstract

This paper concerns the p-maxian problem on trees with an upper bound on the distance of new facilities. We first consider the case $$p = 2$$ p = 2 and show that the optimal objective is obtained if the constraint holds with equality. By this result, we further explore the characteristic of the optimal solution, which helps to develop a linear time algorithm to solve the constrained 2-maxian problem. The result can be extended to the constrained p-maxian on trees based on the nestedness property. We also discuss the constrained p-maxian problem on trees in relation to the unconstrained p-maxian problem and the 1-maxian problem on the underlying tree.

Suggested Citation

  • Trung Kien Nguyen & Nguyen Thanh Hung & Huong Nguyen-Thu, 2020. "A linear time algorithm for the p-maxian problem on trees with distance constraint," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 1030-1043, November.
    • Handle: RePEc:spr:jcomop:v:40:y:2020:i:4:d:10.1007_s10878-020-00650-9
    DOI: 10.1007/s10878-020-00650-9
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    1. Jafar Fathali & Mehdi Zaferanieh, 2023. "The balanced 2-median and 2-maxian problems on a tree," Journal of Combinatorial Optimization, Springer, vol. 45(2), pages 1-16, March.

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