Solving minones-2-sat as Fast as vertex cover

Solving MAXSAT by Solving a Sequence of Simpler SAT Instances

Maxsat is an optimization version of Satisfiability aimed at finding a truth assignment that maximizes the satisfaction of the theory. The technique of solving a sequence of SAT decision problems has been quite successful for solving larger, more industrially focused Maxsat instances, particularly when only a small number of clauses need to be falsified. The SAT decision problems, however, beco...

Solving Minimum Vertex Cover : A Fast Fixed - Parameter - Tra table Algorithm for Pro t Cover ?

Improving Performance in Combinatorial Optimisation Using Averaging and Clustering

In a recent paper an algorithm for solving MAX-SAT was proposed which worked by clustering good solutions and restarting the search from the closest feasible solutions. This was shown to be an extremely effective search strategy, substantially out-performing traditional optimisation techniques. In this paper we extend those ideas to a second classic NP-Hard problem, namely Vertex Cover. Again t...

Faster Randomized Branching Algorithms for $r$-SAT

The problem of determining if an r-CNF boolean formula F over n variables is satisifiable reduces to the problem of determining if F has a satisfying assignment with a Hamming distance of at most d from a fixed assignment α [DGH02]. This problem is also a very important subproblem in Schöning’s local search algorithm for r-SAT [Sch99]. While Schöning described a randomized algorithm solves this...

Paths, Flowers and Vertex Cover

It is well known that in a bipartite (and more generally in a König) graph, the size of the minimum vertex cover is equal to the size of the maximum matching. We first address the question whether (and if not when) this property still holds in a König graph if we insist on forcing one of the two vertices of some of the matching edges in the vertex cover solution. We characterize such graphs usi...