Geometry and Dress groups with non-symmetric cost functions

A metric relation by definition is symmetric. Since many data sets are non-symmetric, in this paper we develop a systematic theory of non-symmetric cost functions. Betweenness relations play an important role. We also introduce the notion of a Dress group in the non-symmetric setting and indicate a notion of curvature.

💡 Research Summary

The paper “Geometry and Dress groups with non‑symmetric cost functions” sets out to replace the classical symmetric metric framework with a theory that accommodates inherently non‑symmetric relations, which appear frequently in modern data analysis, transportation, and computational complexity.

1. Non‑symmetric cost functions.
A cost function (c:S\times S\to