The nestedness property has become an increasingly important means for devising effcient algorithms for network location problems. In this paper we prove that the nestedness property holds for the tactical continuous, and strategic discrete and continuous subtree location problems in a tree network with the ordered median objective, where the λ-weights take at most two different values. These results extend some existing results in the literature. With these nestedness results, we solve the problems in polynomial time. Finally we pose an open problem on identifying the nestedness property for the (k 1; k 2)-trimmed problem.
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机译：嵌套属性已成为为网络位置问题设计有效算法的一种越来越重要的手段。在本文中，我们证明了嵌套属性适用于具有有序中值目标的树形网络中的战术连续，战略离散和连续子树位置问题，其中λ权重最多为两个不同的值。这些结果扩展了文献中已有的一些结果。利用这些嵌套结果，我们可以解决多项式时间内的问题。最后，在确定（k 1; k 2）修剪的问题的嵌套性质时，我们提出了一个开放问题。
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