Corpus ID: 229180907

On the Integrality Gap of Binary Integer Programs with Gaussian Data

  title={On the Integrality Gap of Binary Integer Programs with Gaussian Data},
  author={Sander Borst and D. Dadush and S. Huiberts and Samarth Tiwari},
For a binary integer program (IP) $\max c^{\mathsf T} x, Ax \leq b, x \in \{0,1\}^n$, 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 $1-1/n^7-1/2^{\Omega(m… Expand
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