Published by the Department of Computer Science, The University of Chicago.
gkindler AT cs DOT huji DOT ac DOT il
University of Illinois Urbana-Champaign
Urbana-Champaign, Illinois, USA
akolla AT illinois DOT edu
University of California Berkeley
Berkeley, CA, USA
luca AT berkeley DOT edu
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$(Z_2)$. We conjecture that adding triangle inequalities to the SDP provides a polynomial time algorithm to solve Unique Games on the hypercube.
Submitted September 13,2014, revised February 5, 2015, published
February 7, 2015.