Unique Games on the Hypercube

Naman Agarwal; Guy Kindler; Alexandra Kolla; Luca Trevisan

doi:10.4086/cjtcs.2015.001

Unique Games on the Hypercube

Naman Agarwal, Guy Kindler, Alexandra Kolla, Luca Trevisan

The Rachel and Selim Benin School of Engineering and Computer Science

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we investigate the validity of the Unique Games Conjecture when the constraint graph is the boolean hypercube. We construct an almost optimal integrality gap instance on the Hypercube for the Goemans-Williamson semidefinite program (SDP) for Max-2-LIN(Z2). We conjecture that adding triangle inequalities to the SDP provides a polynomial time algorithm to solve Unique Games on the hypercube.

Original language	English
Journal	Chicago Journal of Theoretical Computer Science
Volume	2015
DOIs	https://doi.org/10.4086/cjtcs.2015.001
State	Published - 2015

Keywords

Unique games
Semi-definite programming
Integrality gap
Hypercube

Access to Document

10.4086/cjtcs.2015.001

http://cjtcs.cs.uchicago.edu/articles/2015/1/contents.html

Cite this

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title = "Unique Games on the Hypercube",

abstract = "In this paper, we investigate the validity of the Unique Games Conjecture when the constraint graph is the boolean hypercube. We construct an almost optimal integrality gap instance on the Hypercube for the Goemans-Williamson semidefinite program (SDP) for Max-2-LIN(Z2). We conjecture that adding triangle inequalities to the SDP provides a polynomial time algorithm to solve Unique Games on the hypercube.",

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AU - Agarwal, Naman

AU - Kindler, Guy

AU - Kolla, Alexandra

AU - Trevisan, Luca

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N2 - In this paper, we investigate the validity of the Unique Games Conjecture when the constraint graph is the boolean hypercube. We construct an almost optimal integrality gap instance on the Hypercube for the Goemans-Williamson semidefinite program (SDP) for Max-2-LIN(Z2). We conjecture that adding triangle inequalities to the SDP provides a polynomial time algorithm to solve Unique Games on the hypercube.

AB - In this paper, we investigate the validity of the Unique Games Conjecture when the constraint graph is the boolean hypercube. We construct an almost optimal integrality gap instance on the Hypercube for the Goemans-Williamson semidefinite program (SDP) for Max-2-LIN(Z2). We conjecture that adding triangle inequalities to the SDP provides a polynomial time algorithm to solve Unique Games on the hypercube.

KW - Unique games

KW - Semi-definite programming

KW - Integrality gap

KW - Hypercube

U2 - 10.4086/cjtcs.2015.001

DO - 10.4086/cjtcs.2015.001

M3 - مقالة

VL - 2015

JO - Chicago Journal of Theoretical Computer Science

JF - Chicago Journal of Theoretical Computer Science

ER -