Connectivity calculus Original Research Article

Given a finite hypergraph H = (V, E) and, for each eϵE, a collection of nonempty subsets πe of e, Möbius inversion is used to establish a recursive formula for the number of connected components of the hypergraph H = (V, ∪eϵEπe). As shown elsewhere, this formula is an essential ingredient in the context of a certain divide-and-conquer strategy that allows us to define a dynamical programming scheme solving Steinerʹs problem for graphs in linear time (however, with a constant depending hyperexponentially on their tree width).