On Integer Programming and Convolution

@article{Jansen2018OnIP,
  title={On Integer Programming and Convolution},
  author={Klaus Jansen and Lars Rohwedder},
  journal={CoRR},
  year={2018},
  volume={abs/1803.04744}
}
Integer programs with a fixed number of constraints can be solved in pseudo-polynomial time. We present a surprisingly simple algorithm and matching conditional lower bounds. Consider an IP in standard form max{cx : Ax = b, x ∈ Zn≥0}, where A ∈ Z , b ∈ Z and c ∈ Z. Let ∆ be an upper bound on the absolute values in A. We show that this IP can be solved in time O(m∆) · log(‖b‖∞). The previous best algorithm has a running time of n ·O(m∆) · ‖b‖1. The hardness of (min, +)-convolution has been used… CONTINUE READING