Combining Treewidth and Backdoors for CSP

Abstract

Decomposition width parameters such as treewidth provide a measurement on the complexity of a graph. Finding a decomposition of smallest width is itself NP-hard but lends itself to a SAT-based solution. Previous work on treewidth, branchwidth and clique-width indicates that identifying a suitable characterization of the considered decomposition method is key for a practically feasible SAT-encoding. In this paper we study SAT-encodings for the decomposition width parameters special treewidth and pathwidth. In both cases we develop SAT-encodings based on two different characterizations. In particular, we develop two novel characterizations for special treewidth based on parti- tions and elimination orderings. We empirically obtained SAT-encodings.