Data mining for cones of metrics, quasi-metrics, hemi-metrics and super-metrics

Details Data mining for cones of metrics, quasi-metrics, hemi-metrics and super-metrics Data mining for cones of metrics, quasi-metrics, hemi-metrics and super-metrics

2002-01-02

arxiv.org/abs/math/0201011v5

Mathematics

Metric Geometry

22 pages, 3 figures

Scientific paper

Using some adaptations of the adjacency decomposition method \cite{CR} and the program {\it cdd} (~\cite{Fu}), we compute the first computationally difficult cases of convex cones of $m$-ary and oriented analogs of semi-metrics and cut semi-metrics, which were introduced in \cite{DR2} and \cite{DP}. We considered also more general notion of $(m,s)$-super-metric and corresponding cones. The data on related cones - the number of facets, of extreme rays, of their orbits and diameters - are collected in Table \ref{tab:MainLovelyTable}. We study also criterion of adjacency for skeletons of those cones and their duals. Some families of extreme rays and operations on them are also given.

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