DROPS

Document

DOI: 10.4230/LIPIcs.CCC.2017.6

The Computational Complexity of Integer Programming with Alternations

Authors: Danny Nguyen and Igor Pak

Published in: LIPIcs, Volume 79, 32nd Computational Complexity Conference (CCC 2017)

Abstract

We prove that integer programming with three alternating quantifiers is NP-complete, even for a fixed number of variables. This complements earlier results by Lenstra and Kannan, which together say that integer programming with at most two alternating quantifiers can be done in polynomial time for a fixed number of variables. As a byproduct of the proof, we show that for two polytopes P, Q in R^4, counting the projection of integer points in Q\P is #P-complete. This contrasts the 2003 result by Barvinok and Woods, which allows counting in polynomial time the projection of integer points in P and Q separately.

Cite as

Danny Nguyen and Igor Pak. The Computational Complexity of Integer Programming with Alternations. In 32nd Computational Complexity Conference (CCC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 79, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{nguyen_et_al:LIPIcs.CCC.2017.6,
  author =	{Nguyen, Danny and Pak, Igor},
  title =	{{The Computational Complexity of Integer Programming with Alternations}},
  booktitle =	{32nd Computational Complexity Conference (CCC 2017)},
  pages =	{6:1--6:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-040-8},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{79},
  editor =	{O'Donnell, Ryan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2017.6},
  URN =		{urn:nbn:de:0030-drops-75151},
  doi =		{10.4230/LIPIcs.CCC.2017.6},
  annote =	{Keywords: Integer Programming, Alternations, Projection of Integer Points}
}

Search Results

Documents authored by Pak, Igor

The Computational Complexity of Integer Programming with Alternations

Abstract

Cite as

Thanks for your feedback!

Could not send message