Multicut Algorithms via Tree Decompositions

Various forms of multicut problems are of great importance in the area of network design. In general, these problems are intractable. However, several parameters have been identified which lead to fixedparameter tractability (FPT). Recently, Gottlob and Lee have proposed the treewidth of the structure representing the graph and the set of pairs of terminal vertices as one such parameter. In this work, we show how this theoretical FPT result can be turned into efficient algorithms for optimization, counting, and enumeration problems in this area.