eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-12-14
7:1
7:20
10.4230/LIPIcs.IPEC.2022.7
article
On the Parameterized Complexity of Computing Tree-Partitions
Bodlaender, Hans L.
1
https://orcid.org/0000-0002-9297-3330
Groenland, Carla
1
https://orcid.org/0000-0002-9878-8750
Jacob, Hugo
2
https://orcid.org/0000-0003-1350-3240
Department of Information and Computing Sciences, Utrecht University, The Netherlands
ENS Paris-Saclay, France
We study the parameterized complexity of computing the tree-partition-width, a graph parameter equivalent to treewidth on graphs of bounded maximum degree.
On one hand, we can obtain approximations of the tree-partition-width efficiently: we show that there is an algorithm that, given an n-vertex graph G and an integer k, constructs a tree-partition of width O(k⁷) for G or reports that G has tree-partition width more than k, in time k^O(1) n². We can improve slightly on the approximation factor by sacrificing the dependence on k, or on n.
On the other hand, we show the problem of computing tree-partition-width exactly is XALP-complete, which implies that it is W[t]-hard for all t. We deduce XALP-completeness of the problem of computing the domino treewidth. Finally, we adapt some known results on the parameter tree-partition-width and the topological minor relation, and use them to compare tree-partition-width to tree-cut width.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol249-ipec2022/LIPIcs.IPEC.2022.7/LIPIcs.IPEC.2022.7.pdf
Parameterized algorithms
Tree partitions
tree-partition-width
Treewidth
Domino Treewidth
Approximation Algorithms
Parameterized Complexity