The integrality number of an integer program

• Published in: Mathematical programming Vol. 192; no. 1-2; pp. 271 - 291
• Main Authors: Paat, Joseph, Schlöter, Miriam, Weismantel, Robert
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2022; Springer; Springer Nature B.V
• Subjects: Calculus of Variations and Optimal Control; Optimization; Combinatorics; Full Length Paper; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematics; Mathematics and Statistics; Mathematics of Computing; Mixed integer; Numerical Analysis; Theoretical; 90C10; 90C11

We introduce the integrality number of an integer program (IP). Roughly speaking, the integrality number is the smallest number of integer constraints needed to solve an IP via a mixed integer (MIP) relaxation. One notable property of this number is its invariance under unimodular transformations of...