no code implementations • 15 Dec 2020 • Sander Borst, Daniel Dadush, Sophie Huiberts, Samarth Tiwari
For a binary integer program (IP) ${\rm max} ~ c^\mathsf{T} x, Ax \leq b, x \in \{0, 1\}^n$, where $A \in \mathbb{R}^{m \times n}$ and $c \in \mathbb{R}^n$ have independent Gaussian entries and the right-hand side $b \in \mathbb{R}^m$ satisfies that its negative coordinates have $\ell_2$ norm at most $n/10$, we prove that the gap between the value of the linear programming relaxation and the IP is upper bounded by $\operatorname{poly}(m)(\log n)^2 / n$ with probability at least $1-2/n^7-2^{-\operatorname{poly}(m)}$.
Optimization and Control Data Structures and Algorithms
