@NiclasJonsson so this is an undergraduate project? is it only yours, no one else working on it? it is very ambitious for a typical undergraduate. you dont explain if the only goal is to implement the algorithm successfully. if you can understand the connection with the optimal treewidth & the algorithm youre implementing, it will help, its explained in the proof. one would likely also need very strong math bkg to be successful.

note, sometimes its possible to email authors to get code, if that is the main goal. have you searched for any code? is the whole idea to implement it yourself? what if there was code elsewhere?