par Bogomolov, Yuri;Fiorini, Samuel 
;Maksimenko, Aleksandr;Pashkovich, Kanstantsin
Référence Discrete & computational geometry, 53, 4, page (809-816)
Publication Publié, 2015-06
;Maksimenko, Aleksandr;Pashkovich, Kanstantsin Référence Discrete & computational geometry, 53, 4, page (809-816)
Publication Publié, 2015-06
Article révisé par les pairs
| Résumé : | We provide an extended formulation of size O(logn)⌊d/2⌋ for the cyclic polytope with dimension d and n vertices (i,i2,…,id), i∈[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≥3. |
