Regular Matroids Have Polynomial Extension Complexity

Manuel Aprile () and Samuel Fiorini ()
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Manuel Aprile: Dipartimento di Matematica, Università degli Studi di Padova, 35121 Padova, Italy
Samuel Fiorini: Département de Mathématique, Université Libre de Bruxelles, B-1050 Brussels, Belgium

Mathematics of Operations Research, 2022, vol. 47, issue 1, 540-559

Abstract: We prove that the extension complexity of the independence polytope of every regular matroid on n elements is O ( n 6 ) . Past results of Wong and Martin on extended formulations of the spanning tree polytope of a graph imply a O ( n 2 ) bound for the special case of (co)graphic matroids. However, the case of a general regular matroid was open, despite recent attempts. We also consider the extension complexity of circuit dominants of regular matroids, for which we give a O ( n 2 ) bound.

Keywords: Primary: 90C27; 52B40; extended formulations; regular matroids; independence polytope; spanning tree polytope; cut dominant (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:47:y:2022:i:1:p:540-559

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