Linear programming, width-1 CSPs, and robust satisfaction

Authors:
Gabor Kun;Ryan O'Donnell;Suguru Tamaki;Yuichi Yoshida;Yuan Zhou
Affiliations:
Institute for Advanced Study, and DIMACS;Carnegie Mellon University;Kyoto University;Kyoto University, and Preferred Infrastructure, Inc.;Carnegie Mellon University
Venue:
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Year:
2012

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Abstract

We say that an algorithm robustly decides a constraint satisfaction problem Π if it distinguishes at-least-(1 -ε)-satisfiable instances from less-than-(1 - r(ε))-satisfiable instances for some function r(ε) with r(ε) → 0 as ε → 0. In this paper we show that the canonical linear programming relaxation robustly decides Π if and only if Π has "width 1" (in the sense of Feder and Vardi).