Cartesian Factoring of Polyhedra in Linear Relation Analysis

Linear Relation Analysis [CH78] suffers from the cost of operations on convex polyhedra, which can be exponential with the number of involved variables. In order to reduce this cost, we propose to detect when a polyhedron is a Cartesian product of polyhedra of lower dimensions, i.e., when groups of variables are unrelated with each other. Classical operations are adapted to work on such factored polyhedra. Our implementation shows encouraging experimental results.