Understanding parallel repetition requires understanding foams

Uriel Feige*, Guy Kindler, Ryan O'Donnell

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

33 Scopus citations

Abstract

Motivated by the study of Parallel Repetition and also by the Unique Games Conjecture, we investigate the value of the "Odd Cycle Games" under parallel repetition. Using tools from discrete harmonic analysis, we show that after d rounds on the cycle of length m, the value of the game is at most 1 - (1/m) · Ω̃U(√d) (for d ≤ m2, say). This beats the natural barrier of 1 - ⊖(1/m)2 · d for Raz-style proofs [31, 21 j (see [11]) and also the SDP bound of Feige-Lovász [14, 17]; however, it just barely fails to have implications for Unique Games. On the other hand, we also show that improving our bound would require proving nontrivial lower bounds on the surface area of high-dimensional foams. Specifically, one would need to answer: What is the least surface area of a cell that tiles ℝd by the lattice ℤd ?

Original languageAmerican English
Title of host publicationProceedings - Twenty-Second Annual IEEE Conference on Computational Complexity, CCC 2007
Pages179-192
Number of pages14
DOIs
StatePublished - 2007
Externally publishedYes
Event22nd Annual IEEE Conference on Computational Complexity, CCC 2007 - San Diego, CA, United States
Duration: 13 Jun 200716 Jun 2007

Publication series

NameProceedings of the Annual IEEE Conference on Computational Complexity
ISSN (Print)1093-0159

Conference

Conference22nd Annual IEEE Conference on Computational Complexity, CCC 2007
Country/TerritoryUnited States
CitySan Diego, CA
Period13/06/0716/06/07

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