Papers › On Integer Programming, Discrepancy, and Convolution
On Integer Programming, Discrepancy, and Convolution
Klaus Jansen, Lars Rohwedder
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Integer programs with m constraints are solvable in pseudo-polynomial time in Δ, the largest coefficient in a constraint, when m is a fixed constant. We give a new algorithm with a running time of O(√(m)Δ)²ᵐ + O(nm), which improves on the state-of-the-art. Moreover, we show that improving on our algorithm for any m is equivalent to improving over the quadratic time algorithm for (min, +)-convolution. This is a strong evidence that our algorithm's running time is the best possible. We also present a specialized algorithm with running time O(√(m) Δ)^((1 + o(1))m) + O(nm) for testing feasibility of an integer program and also give a tight lower bound, which is based on the SETH in this case.
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