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arXiv · 2212.11239

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

Alberto Del Pia·Aida Khajavirad
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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.

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Alberto Del Pia, Aida Khajavirad. 2022-12-15. A polynomial-size extended formulation for the multilinear polytope of beta-acyclic hypergraphs. https://arxiv.org/abs/2212.11239

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