For this reason, in the following discussion we use as a term of comparison quantity tw(D), the treewidth of D. When processing D , the running time of Algorithm 2 depends on tw(LG(D )), the treewidth of the line graph of D , which in turn depends on the choice of the binarization of D. There are several ways in which we can binarize D, resulting in different values of tw(LG(D )).
a bad choice of binarization for D may result in tw(LG(D )) much larger than tw(D).