publication . Other literature type . Preprint . 2018 . Embargo end date: 24 May 2018

Computational Topology and the Unique Games Conjecture

Grochow, Joshua A.; Tucker-Foltz, Jamie;
Open Access English
  • Published: 19 Mar 2018
  • Publisher: Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Wadern/Saarbruecken, Germany
Abstract
Covering spaces of graphs have long been useful for studying expanders (as "graph lifts") and unique games (as the "label-extended graph"). In this paper we advocate for the thesis that there is a much deeper relationship between computational topology and the Unique Games Conjecture. Our starting point is Linial's 2005 observation that the only known problems whose inapproximability is equivalent to the Unique Games Conjecture - Unique Games and Max-2Lin - are instances of Maximum Section of a Covering Space on graphs. We then observe that the reduction between these two problems (Khot-Kindler-Mossel-O'Donnell, FOCS 2004; SICOMP, 2007) gives a well-defined map ...
Subjects
arXiv: Computer Science::Computer Science and Game Theory
free text keywords: Computer Science, 000 Computer science, knowledge, general works, Computer Science - Computational Complexity, Computer Science - Computational Geometry, Computer Science - Discrete Mathematics, Mathematics - Algebraic Topology, 68Q25, 52C45, 68U05, 57M10, 68W25, 05C10, F.2.2
Related Organizations
Funded by
NSF| Collaborative Research: New Algorithms for Group Isomorphism
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1750319
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
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