# A Computational Status Update for Exact Rational Mixed Integer Programming

arXiv: https://arxiv.org/abs/2101.09141 · HTML: https://mlsanity.com/paper/2101.09141/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jan 2021.

## Built on by (most cited first, 3 of 3)

- [Certified Symmetry and Dominance Breaking for Combinatorial Optimisation](https://mlsanity.com/paper/2203.12275/) (2022)
- [Efficient and Reliable Hitting-Set Computations for the Implicit Hitting Set Approach](https://mlsanity.com/paper/2508.07015/) (2025)
- [REMS: a unified solution representation, problem modeling and metaheuristic algorithm design for general combinatorial optimization problems](https://mlsanity.com/paper/2505.17108/) (2025)

## Abstract (arXiv)

The last milestone achievement for the roundoff-error-free solution of general mixed integer programs over the rational numbers was a hybrid-precision branch-and-bound algorithm published by Cook, Koch, Steffy, and Wolter in 2013. We describe a substantial revision and extension of this framework that integrates symbolic presolving, features an exact repair step for solutions from primal heuristics, employs a faster rational LP solver based on LP iterative refinement, and is able to produce independently verifiable certificates of optimality. We study the significantly improved performance and give insights into the computational behavior of the new algorithmic components. On the MIPLIB 2017 benchmark set, we observe an average speedup of 6.6x over the original framework and 2.8 times as many instances solved within a time limit of two hours.