I'm looking for an up to date reference for parameterized complexity of tree and branch decompositions. IE, complexity of finding tree/branch decomposition of optimal width in terms of relevant graph parameters (treewidth, branchwidth, graph size)
Somewhat related, this paper from 2021 gives results for rankwidth, looking for equivalent for treewidth/branchwidth (also this for SOTA of treewidth 2-approximation). Any references appreciated!
