Cones of Weighted and Partial Metrics
Abstract
A partial semimetric on V_n={1, ..., n} is a function f=((f_{ij})): V_n^2 -> R_>=0 satisfying f_ij=f_ji >= f_ii and f_ij+f_ik-f_jk-f_ii >= 0 for all i,j,k in V_n. The function f is a weak partial semimetric if f_ij >= f_ii is dropped, and it is a strong partial semimetric if f_ij >= f_ii is complemented by f_ij <= f_ii+f_jj. We describe the cones of weak and strong partial semimetrics via corresponding weighted semimetrics and list their 0,1-valued elements, identifying when they belong to extreme rays. We consider also related cones, including those of partial hypermetrics, weighted hypermetrics, l_1-quasi semimetrics and weighted/partial cuts.
Keywords
Cite
@article{arxiv.1101.0517,
title = {Cones of Weighted and Partial Metrics},
author = {Michel Deza and Elena Deza and Janoš Vidali},
journal= {arXiv preprint arXiv:1101.0517},
year = {2011}
}
Comments
21 pages, 4 tables, 2 figures; To be submitted to Proc. of the Conference in the honor of Prof. K.P.Shum