A new point of NP-hardness for unique games

d abstract; full version begins on page 13) Ryan O’Donnell∗ John Wright† November 2, 2011 We show that distinguishing 1 2 -satisfiable Unique-Games instances from (3 8 + )-satisfiable instances is NP-hard (for all > 0). A consequence is that we match or improve the best known c vs. s NP-hardness result for Unique-Games for all values of c (except for c very close to 0). For these c, ours is the first hardness result showing that it helps to take the alphabet size larger than 2. Our NP-hardness reductions are quasilinear-size and thus show nearly full exponential time is required, assuming the ETH. ∗ Department of Computer Science, Carnegie Mellon University. Supported by NSF grants CCF-0747250 and CCF-0915893, and by a Sloan fellowship. Some of this research performed while the author was a von Neumann Fellow at the Institute for Advanced Study, supported by NSF grants DMS-083537 and CCF-0832797. † Department of Computer Science, Carnegie Mellon University. 

• Type: Journal
• Year: 2012
• Where: STOC
• Authors: Ryan O'Donnell, John Wright
• Keywords: Algorithms, Alphabet Size, Carnegie Mellon University, Sloan Fellowship, STOC 2012