research-article

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

Authors:

Samuel Fiorini,

Sebastian Pokutta,

Hans Raj Tiwary,

Ronald de WolfAuthors Info & Claims

STOC '12: Proceedings of the forty-fourth annual ACM symposium on Theory of computing

Pages 95 - 106

https://doi.org/10.1145/2213977.2213988

Published: 19 May 2012 Publication History

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.

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Index Terms

Linear vs. semidefinite extended formulations: exponential separation and strong lower bounds
1. Theory of computation
  1. Randomness, geometry and discrete structures

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cover image ACM Conferences

STOC '12: Proceedings of the forty-fourth annual ACM symposium on Theory of computing

May 2012

1310 pages

ISBN:9781450312455

DOI:10.1145/2213977

General Chair:
Howard Karloff
AT&T Labs--Research
,
Program Chair:
Toniann Pitassi
University of Toronto

Copyright © 2012 ACM.

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Published: 19 May 2012

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May 19 - 22, 2012

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Sun WWei FShao YWei Z(2024)Sudden death of quantum advantage in correlation generationsScience Advances10.1126/sciadv.adr500210:47Online publication date: 22-Nov-2024
https://doi.org/10.1126/sciadv.adr5002
Chen ZLin LLin XWei ZYao P(2024)The Generations of Classical Correlations via Quantum SchemesIEEE Transactions on Information Theory10.1109/TIT.2024.339134170:6(4160-4169)Online publication date: Jun-2024
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