The recently introduced graph parameter tree-cut width plays a similar role with respect to immersions as the graph parameter treewidth plays with respect to minors. In this paper we provide the first algorithmic applications of tree-cut width to hard combinatorial problems. Tree-cut width is known to be lower-bounded by a function of treewidth, but it can be much larger and hence has the potential to facilitate the efficient solution of problems which are not known to be fixed-parameter tractable (FPT) when parameterized by treewidth. We introduce the notion of nice tree-cut decompositions and provide FPT algorithms for the showcase problems CAPACITATED VERTEX COVER, CAPACITATED DOMINATING SET AND IMBALANCE parameterized by the tree-cut width of an input graph G. On the other hand, we show that LIST COLORING, PRECOLORING EXTENSION AND BOOLEAN CSP (the latter parameterized by the tree-cut width of the incidence graph) are W[1]-hard and hence unlikely to be fixed-parameter tractable when parameterized by tree-cut width.
CITATION STYLE
Ganian, R., Kim, E. J., & Szeider, S. (2015). Algorithmic applications of tree-cut width. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9235, pp. 348–360). Springer Verlag. https://doi.org/10.1007/978-3-662-48054-0_29
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