Cones of weighted quasi-metrics, weighted quasi-hypermetrics and of oriented cuts

Abstract

We show that the cone of weighted n-point quasi-metrics WQMetn, the cone of weighted quasi-hypermetrics WHypn and the cone of oriented cuts OCutn are projec- tions along an extreme ray of the metric cone Metn+1, of the hypermetric cone Hypn+1 and of the cut cone Cutn+1, respectively. This projection is such that if one knows all faces of an original cone then one knows all faces of the projected cone.

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