On the Integrality Gap of Binary Integer Programs with Gaussian Data
@article{Borst2020OnTI, title={On the Integrality Gap of Binary Integer Programs with Gaussian Data}, author={Sander Borst and D. Dadush and S. Huiberts and Samarth Tiwari}, journal={ArXiv}, year={2020}, volume={abs/2012.08346} }
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… CONTINUE READING
References
SHOWING 1-10 OF 14 REFERENCES
Proximity results and faster algorithms for Integer Programming using the Steinitz Lemma
- Computer Science, Mathematics
- SODA
- 2018
- 45
- PDF
Branch-and-Bound Solves Random Binary Packing IPs in Polytime
- Mathematics, Computer Science
- ArXiv
- 2020
- 2
- Highly Influential
- PDF
Minkowski's Convex Body Theorem and Integer Programming
- Mathematics, Computer Science
- Math. Oper. Res.
- 1987
- 656
- PDF
On finding the exact solution of a zero-one knapsack problem
- Mathematics, Computer Science
- STOC '84
- 1984
- 46