Optimal 2-constraint satisfaction via sum-product algorithms

We show that for a given set of m pairwise constraints over n variables, a variable assignment that satisfies maximally many m constraints (MAX-2-CSP) can be found in O(nm dn/3) time, where d is the maximum number of states per variable, and < 2.376 is the matrix product exponent over a ring; the notation O suppresses factors polylogarithmic in m and n. As a corollary, MAX-2-SAT can be solved in

• Type: Journal
• Year: 2006
• Where: IPL
• Authors: Mikko Koivisto
• Keywords: IPL 2006, Matrix Product Exponent, Maximum Number, Variable Assignment