Linear vs. semidefinite extended formulations: exponential separation and strong lower bounds

Authors
  • S. Fiorini
  • S. Massar
  • S. Pokutta
  • H.R. Tiwary
Publication date 2012
Book title STOC'12
Book subtitle 2012 ACM Symposium on Theory of Computing : May 19-22, 2012, New York, New York, USA
ISBN (electronic)
  • 9781450312455
Event 44th annual ACM Symposium on Theory of Computing
Pages (from-to) 95-106
Publisher New York: ACM
Organisations
  • Interfacultary Research - Institute for Logic, Language and Computation (ILLC)
Abstract We solve a 20-year old problem posed by Yannakakis and prove that there exists no polynomial-size linear program (LP) whose associated polytope projects to the traveling salesman polytope, even if the LP is not required to be symmetric. Moreover, we prove that this holds also for the cut polytope and the stable set polytope. These results were discovered through a new connection that we make between one-way quantum communication protocols and semidefinite programming reformulations of LPs.
Document type Conference contribution
Language English
Published at
https://doi.org/10.1145/2213977.2213988 (Final published version)
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