# Fine-grained complexity of integer programming: The case of bounded branch-width and rank

@article{Fomin2016FinegrainedCO, title={Fine-grained complexity of integer programming: The case of bounded branch-width and rank}, author={F. Fomin and Fahad Panolan and M. S. Ramanujan and Saket Saurabh}, journal={ArXiv}, year={2016}, volume={abs/1607.05342} }

We use the Exponential Time and Strong Exponential Time hypotheses (ETH & SETH) to provide conditional lower bounds on the solvability of the integer programming (IP) problem. We provide evidence that the running times of known pseudo-polynomial time algorithms solving IP, when the number of constraints is a constant [Papadimitriou, J. ACM 1981] and when the branch-width of the corresponding column-matroid is a constant [Cunningham and Geelen, IPCO 2007], are probably optimal. ∗Department of…

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