On Integer Programming and Convolution

Authors Klaus Jansen, Lars Rohwedder

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Author Details

Klaus Jansen
  • Department of Computer Science, Kiel University, Kiel, Germany
Lars Rohwedder
  • Department of Computer Science, Kiel University, Kiel, Germany

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Klaus Jansen and Lars Rohwedder. On Integer Programming and Convolution. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 43:1-43:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Integer programs with a constant number of constraints are solvable in pseudo-polynomial time. We give a new algorithm with a better pseudo-polynomial running time than previous results. Moreover, we establish a strong connection to the problem (min, +)-convolution. (min, +)-convolution has a trivial quadratic time algorithm and it has been conjectured that this cannot be improved significantly. We show that further improvements to our pseudo-polynomial algorithm for any fixed number of constraints are equivalent to improvements for (min, +)-convolution. This is a strong evidence that our algorithm's running time is the best possible. We also present a faster specialized algorithm for testing feasibility of an integer program with few constraints and for this we also give a tight lower bound, which is based on the SETH.

Subject Classification

ACM Subject Classification
  • Theory of computation → Integer programming
  • Theory of computation → Dynamic programming
  • Integer programming
  • convolution
  • dynamic programming
  • SETH


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