A polynomial-size extended formulation for the multilinear polytope of beta-acyclic hypergraphs

TL;DR

This paper presents a polynomial-size extended formulation for the multilinear polytope of beta-acyclic hypergraphs, advancing understanding of their geometric structure and computational properties.

Contribution

It provides the first polynomial-size extended formulation for the multilinear polytope of beta-acyclic hypergraphs, linking hypergraph acyclicity to polyhedral complexity.

Findings

Polynomial-size extended formulation for beta-acyclic hypergraphs

Characterization of hypergraphs with such formulations

Insights into the facial structure of multilinear polytopes

Abstract

We consider the multilinear polytope defined as the convex hull of the set of binary points satisfying a collection of multilinear equations. The complexity of the facial structure of the multilinear polytope is closely related to the acyclicity degree of the underlying hypergraph. We obtain a polynomial-size extended formulation for the multilinear polytope of beta-acyclic hypergraphs, hence characterizing the acyclic hypergraphs for which such a formulation can be constructed.