Corpus ID: 229180907

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… Expand
1 Citations
Lower Bounds on the Size of General Branch-and-Bound Trees
  • PDF

References

SHOWING 1-10 OF 14 REFERENCES
Proximity results and faster algorithms for Integer Programming using the Steinitz Lemma
  • 45
  • PDF
On Integer Programming, Discrepancy, and Convolution
  • 9
Branch-and-Bound Solves Random Binary Packing IPs in Polytime
  • 2
  • Highly Influential
  • PDF
Smoothed Analysis of Integer Programming
  • 19
  • Highly Influential
  • PDF
Minkowski's Convex Body Theorem and Integer Programming
  • R. Kannan
  • Mathematics, Computer Science
  • Math. Oper. Res.
  • 1987
  • 659
Probabilistic analysis of knapsack core algorithms
  • 22
  • PDF
An Introduction To Probability Theory And Its Applications
  • 10,848
  • PDF
On finding the exact solution of a zero-one knapsack problem
  • 46
On the Average Difference between the Solutions to Linear and Integer Knapsack Problems
  • 33
On the complexity of integer programming
  • 476
  • PDF
...
1
2
...