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.

本文涉及具有新设施距离上限的树上的p -maxian问题。我们首先考虑情况\（p = 2 \）并表明，如果约束条件相等，则可获得最佳目标。通过此结果，我们进一步探索了最优解的特征，这有助于开发线性时间算法来解决约束2-maxian问题。可以基于nestedness属性将结果扩展到树上的约束p -maxian。我们还讨论了限制p上相对于不受约束的树木-maxian问题p -maxian问题和潜在的树1麻线问题。