A Geometric Study of the Split Decomposition

10 years 6 months ago
A Geometric Study of the Split Decomposition
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 functions, 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. Using our approach, the split decomposition of metrics can be naturally extended to distance functions, which may violate the triangle inequality, using partial split distances.
Hiroshi Hirai
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Where DCG
Authors Hiroshi Hirai
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