License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2019.43
URN: urn:nbn:de:0030-drops-101365
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/10136/
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Jansen, Klaus ; Rohwedder, Lars

On Integer Programming and Convolution

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LIPIcs-ITCS-2019-43.pdf (0.5 MB)

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.

BibTeX - Entry

@InProceedings{jansen_et_al:LIPIcs:2018:10136,
  author =	{Klaus Jansen and Lars Rohwedder},
  title =	{{On Integer Programming and Convolution}},
  booktitle =	{10th Innovations in Theoretical Computer Science  Conference (ITCS 2019)},
  pages =	{43:1--43:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-095-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{124},
  editor =	{Avrim Blum},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/10136},
  URN =		{urn:nbn:de:0030-drops-101365},
  doi =		{10.4230/LIPIcs.ITCS.2019.43},
  annote =	{Keywords: Integer programming, convolution, dynamic programming, SETH}
}

Keywords: Integer programming, convolution, dynamic programming, SETH
Collection: 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)
Issue Date: 2018
Date of publication: 08.01.2019

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