Hard constraint satisfaction problems have hard gaps at location 1

An instance of the maximum constraint satisfaction problem (Max CSP) is a nite collection of constraints on a set of variables, and the goal is to assign values to the variables that maximises the number of satised constraints. Max CSP captures many well-known problems (such as Max k-SAT and Max Cut) and is consequently NP-hard. Thus, it is natural to study how restrictions on the allowed constraint types (or constraint language) aect the complexity and approximability of Max CSP. The PCP theorem is equivalent to the existence of a constraint language for which Max CSP has a hard gap at location 1, i.e. it is NP-hard to distinguish between satisable instances and instances where at most some constant fraction of the constraints are satisable. All constraint languages, for which the CSP problem (i.e., the problem of deciding whether all constraints can be satised) is currently known to be NP-hard, have a certain algebraic property. We prove that any constraint language with this ...

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Peter Jonsson, Andrei A. Krokhin, Fredrik Kuivinen
• Keywords: Constraint Type, CORR 2007, Education, Max CSP, Maximum Constraint Satisfaction