Branch and Recharge: Exact Algorithms for Generalized Domination

In this paper we present branching algorithms for infinite classes of problems. The novelty in the design and analysis of our branching algorithms lies in the fact that the weights are redistributed over the graph by the algorithms. Our particular setting to make this idea work is a combination of a branching approach with a recharging mechanism. We call it Branch & Recharge. To demonstrate this approach we consider a generalized domination problem. Let σ and ρ be two nonempty sets of nonnegative integers. A vertex subset S⊆V of an undirected graph G=(V(G),E(G)) is called a (σ,ρ)‐dominating set of G if |N(v)∩S|∈σ for all v∈S and |N(v)∩S|∈ρ for all v∈V\S. This notion generalizes many domination‐type graph invariants.