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On Integer Programming and Convolution

Authors Klaus Jansen, Lars Rohwedder

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LIPIcs.ITCS.2019.43.pdf
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Subject Classification

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

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Abstract

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.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.ITCS.2019.43

Author Details

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

Funding

Research was supported by German Research Foundation (DFG) projects JA 612/20-1 and JA 612/16-1.

References

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