A Minimal Set of Shannon-type Inequalities for MRF Structures with Functional Dependencies
Terence Chan, Satyajit Thakor, Alex J. Grant · 2018
The minimal set of Shannon-type inequalities, called elemental inequalities, plays a central role in efficiently determining whether a given inequality is in fact Shannon-type or not and in computing the linear programming bound for network coding capacity. In previous work we characterised a minimal set when functional dependence constraints are present. In this work we further generalize the characterisation to include Markov random field (MRF) structures which are defined by full conditional mutual independence constraints.