负边权的一维极小填充
One-dimensional minimal fillings with negative edge weights
摘要：
Ivanov和Tuzhilin开始研究Gromov极小填充问题的一个特殊情况（推广到分层流形的情况）。利用具有非负权函数的权图作为有限度量空间的极小填充。本文引入广义极小填充，即权函数不一定非负的极小填充。证明了对于任何有限的度量空间，其最小填充在该空间的所有广义填充类中具有最小权。
英文摘要：
Ivanov and Tuzhilin started an investigation of a particular case of Gromov Minimal Fillings problem (generalized to the case of stratified manifolds). Weighted graphs with non-negative weight function were used as minimal fillings of finite metric spaces. In the present paper we introduce generalized minimal fillings, i.e. minimal fillings where the weight function is not necessarily non-negative. We prove that for any finite metric space its minimal filling has the minimum weight in the class of all generalized fillings of the space.
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