Linear programming, width-1 CSPs, and robust satisfaction

Gábor Kun, Ryan O'Donnell, Suguru Tamaki, Yuichi Yoshida, Yuan Zhou

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).