Abstract: We showthat the cone ofweighted n-point quasi-metricsWQMetn, the cone ofweighted quasi-hypermetrics WHypn and the cone of oriented cuts OCutn are projections 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.

Keywords: distance, metrics, hypermetrics, cutmetrics, quasi-metrics.

MSC: 52B12, 51F99, 90C57

Link:

CONES OF WEIGHTED QUASIMETRICS,WEIGHTED QUASIHYPERMETRICS AND OF ORIENTED CUTS

Michel Deza,Vyacheslav P.Grishukhin,Elena Deza

http://www.foibg.com/ibs_isc/ibs-25/ibs-25-p04.pdf