Faster exact algorithms for some terminal set problems

Many problems on graphs can be expressed in the following language: given a graph G=(V,E) and a terminal set T⊆V, find a minimum size set S⊆V which intersects all “structures” (such as cycles or paths) passing through the vertices in T. We refer to this class of problems as terminal set problems. In this paper, we introduce a general method to obtain faster exact exponential time algorithms for several terminal set problems. In the process, we break the O⁎(2n) barrier for the classic Node Multiway Cut, Directed Unrestricted Node Multiway Cut and Directed Subset Feedback Vertex Set problems.