Robustly Solvable Constraint Satisfaction Problems

TL;DR

This paper confirms Guruswami and Zhou's conjecture by characterizing the constraint languages for which robust algorithms efficiently solve nearly satisfiable constraint satisfaction problems.

Contribution

It provides a proof of the conjecture, establishing a clear characterization of constraint languages with robust solvability.

Findings

Confirmed Guruswami and Zhou's conjecture

Characterized constraint languages with robust algorithms

Established conditions for efficient robust CSP solving

Abstract

An algorithm for a constraint satisfaction problem is called robust if it outputs an assignment satisfying at least $(1-g(\varepsilon))$-fraction of the constraints given a $(1-\varepsilon)$-satisfiable instance, where $g(\varepsilon) \rightarrow 0$ as $\varepsilon \rightarrow 0$. Guruswami and Zhou conjectured a characterization of constraint languages for which the corresponding constraint satisfaction problem admits an efficient robust algorithm. This paper confirms their conjecture.