Geometric Study on the Split Decomposition of Finite Metrics ∗
Geometric Study on the Split Decomposition of Finite Metrics ∗
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有限度量分裂分解的几何研究*
DOI：
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发表时间：
2004
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通讯作者：
H. Hirai
中科院分区：
文献类型：
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作者：
H. Hirai
本文从凸分析和多面体几何的观点出发，对分裂分解理论和T-理论作了新的解释。通过将有限度量看作离散凹函数，Bandelt-Dress分裂分解可以作为本文所介绍的多面体/离散凹函数的更一般分解的一种特殊情况。它示出的组合学的分裂讨论连接到分裂分解对应于超平面安排和一个点配置的几何性质。通过我们的方法，分裂分解的度量可以自然地扩展到距离函数，这可能违反三角不等式，使用部分分裂距离。
This paper sheds a new light on the split decomposition theory and T-theory from the viewpoint of convex analysis and polyhedral geometry. By regarding finite metrics as discrete concave function, Bandelt-Dress’ split decomposition can be derived as a special case of more general decomposition of polyhedral/discrete concave functions introduced in this paper. It is shown that the combinatorics of splits discussed in connection to the split decomposition corresponds to the geometric properties of a hyperplane arrangement and a point configuration. By our approach, the split decomposition of metrics can be naturally extended for distance functions, which may violate the triangle inequality, using partial split distances.