On the parameterized complexity of separating certain sources from the target
Résumé
multicut is proven to be FPT parameterized by the size of the cutset p. We focus on its generalization partial multicut setting the number of pairs of terminals to be separated as a parameter r: it asks for the minimum edge/vertex cut whose removal would separate r sources si from their target ti. Our main contributions concern its single target subproblem, partial one-target cut (potc). We show that potc, when edges are to be cut, is FPT parameterized by the cutset size p but is W[1]-hard when parameterized only with r. The vertex-cutting version of potc is W[1]-hard regardless of parameter configurations involving r and p.