Diameters of the Characteristic Imset Polytopes

TL;DR

This paper investigates the diameters of characteristic imset polytopes, providing polynomial bounds that relate to causal discovery and the connectivity of these polytopes.

Contribution

It introduces low-degree polynomial bounds on the diameters of characteristic imset polytopes and their faces, advancing understanding of their geometric structure.

Findings

Polynomial bounds on the diameter of CIM_n

Polynomial bounds on the diameter of CIM_G

Insights into the connectivity of characteristic imset polytopes

Abstract

It has been shown that the edge structure of the characteristic imset polytope is closely connected to the question of causal discovery. The diameter of a polytope is an indicator of how connected the polytope is and moreover gives us a hypothetical worst case scenario for an edge-walk over the polytope. We present low-degree polynomial bounds on the diameter of $\operatorname{CIM}_n$ and, for any given undirected graph $G$, the face $\operatorname{CIM}_G$.