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14-09-2020 | Issue 4/2020

Journal of Combinatorial Optimization 4/2020

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

Journal:
Journal of Combinatorial Optimization > Issue 4/2020
Authors:
Trung Kien Nguyen, Nguyen Thanh Hung, Huong Nguyen-Thu
Important notes
This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.01-2019.325.

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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 \(p = 2\) 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.

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