Branching and Treewidth Based Exact Algorithms

Abstract

Branch & Reduce and dynamic programming on graphs of bounded treewidth are among the most common and powerful techniques used in the design of exact (exponential time) algorithms for NP hard problems. In this paper we discuss the efficiency of simple algorithms based on combinations of these techniques. We give several examples of possible combinations of branching and programming which provide the fastest known algorithms for a number of NP hard problems: Minimum Maximal Matching and some variations, counting the number of maximum weighted independent sets. We also briefly discuss how similar techniques can be used to design parameterized algorithms. As an example, we give fastest known algorithm solving k-Weighted Vertex Cover problem.