AI 中文总结
该研究针对有限度量空间的最小参数化广义填充问题，为连接度量空间的每棵树构造凸多面体，证明多面体顶点集的并集构成极值子集，明确了最小填充权重的计算方式。
AI 中文摘要
有限度量空间M的最小参数化广义填充问题（最优连接问题的一种形式），对应于为连接M的每棵树G（作为参数化填充的类型）构造凸多维多面体W_G。参数化最小填充的权重可通过M的距离向量对应的特殊线性函数在W_G上的最大值求得。研究证明，所有可能的G对应的多面体W_G的顶点集的并集构成一个极值子集，即与其凸包的顶点集重合。
英文摘要
Problem of minimal parametric generalized fillings of finite metric space $M$ (a version of optimal connection problem) leads to construction of a convex multidimensional polyhedra $W_G$ for each tree $G$ connecting $M$ chosen as type of the parametric filling. The weight of the parametric minimal filling can be found as maximum on $W_G$ of the special linear function corresponding to the distance vector of $M$. It is proved that the union of vertex sets of the polyhedra $W_G$ over all possible $G$ forms an extremal subset, i.e., coincides with the vertex set of its convex hull.
