New Upper Bounds for MAX-2-SAT and MAX-2-CSP w.r.t. the Average Variable Degree

Exact Max 2-Sat: Easier and Faster

Prior algorithms known for exactly solving Max 2-Sat improve upon the trivial upper bound only for very sparse instances. We present new algorithms for exactly solving (in fact, counting) weighted Max 2-Sat instances. One of them has a good performance if the underlying constraint graph has a small separator decomposition, another has a slightly improved worst case performance. For a 2-Sat inst...

New exact algorithms for the 2-constraint satisfaction problem

Many optimization problems can be phrased in terms of constraint satisfaction. In particular MAX-2SAT and MAX-2-CSP are known to generalize many hard combinatorial problems on graphs. Algorithms solving the problem exactly have been designed but the running time is improved over trivial brute-force solutions only for very sparse instances. Despite many efforts, the only known algorithm [29] sol...

Local Maxima and Improved Exact Algorithm for MAX-2-SAT

Given a MAX-2-SAT instance, we define a local maximum to be an assignment such that changing any single variable reduces the number of satisfied clauses. We consider the question of the number of local maxima that an instance of MAX-2-SAT can have. We give upper bounds in both the sparse and nonsparse case, where the sparse case means that there is a bound d on the average number of clauses inv...

New Worst-Case Upper Bounds for MAX-2-SAT with Application to MAX-CUT

Solving Sparse Semi-Random Instances of Max Cut and Max CSP in Linear Expected Time

We show that a maximum cut of a random graph below the giantcomponent threshold can be found in linear space and linear expected time by a simple algorithm. In fact, the algorithm solves a more general class of problems, namely binary 2-variable-constraint satisfaction problems, or Max 2-CSPs. In addition to Max Cut, Max 2-CSPs encompass Max Dicut, Max 2-Lin, Max 2-Sat, Max-Ones-2-Sat, maximum ...