Lecture 13 Constraint Satisfaction Problems

Max-3-SAT. In this problem, the domain is {0, 1}; a collection of constraint types are disjunctions of the form {xi∨xj ∨xk, xi∨xj ∨xk, xi∨xj ∨xk, . . . , xi∨xj ∨xk, xi∨xj, . . . , xi∨ xj, xi, xi} resulting in total of 14 constraint types. Max-Cut. Here, the domain is again {0, 1}, the collection of constraint types is simply {vi 6= vj}. Intuitively, we have one such constraint for each edge in a given Max-Cut instance, and the goal is to label the vertices.