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

Abstract

We show that the cone of weighted n-point quasi-metrics W QM et n , the cone of weighted quasi-hypermetrics W Hyp n and the cone of oriented cuts OCut n are projections along an extreme ray of the metric cone M et n+1 , of the hypermetric cone Hyp n+1 and of the cut cone Cut n+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.