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arXiv · 1401.8138

Small Extended Formulations for Cyclic Polytopes

Yuri Bogomolov·Samuel Fiorini·Aleksandr Maksimenko·Kanstantsin Pashkovich
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Abstract

We provide an extended formulation of size O(log n)^{\lfloor d/2 \rfloor} for the cyclic polytope with dimension d and n vertices (i,i^2,\ldots,i^d), i in [n]. First, we find an extended formulation of size log(n) for d= 2. Then, we use this as base case to construct small-rank nonnegative factorizations of the slack matrices of higher-dimensional cyclic polytopes, by iterated tensor products. Through Yannakakis's factorization theorem, these factorizations yield small-size extended formulations for cyclic polytopes of dimension d>2.

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Yuri Bogomolov, Samuel Fiorini, Aleksandr Maksimenko, Kanstantsin Pashkovich. 2015-02-20. Small Extended Formulations for Cyclic Polytopes. https://doi.org/10.1007/s00454-015-9682-1

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