Proof of `Optimal Tree Decompositions from a Given One`
What this proof establishes
no assumptions
Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.
In the paper
- page 2 of this submission's paper
Description
The improvement step of Bodlaender–Kloks on a word RAM: given a nice decomposition of width it returns one of width at most or , proved by a dispatcher over the same exact algorithm (if the given decomposition is returned; otherwise the main algorithm runs on the graph and ).