An approximation algorithm for the k-generalized Steiner forest problem - Gao, Jiawen; Gao, Suogang; Liu, Wen; Wu, Weili; Du, Ding-Zhu; Hou, Bo (Optimization letters, 2021)
In this paper, we introduce the k -generalized Steiner forest ( k -GSF) problem, which is a natural generalization of the k -Steiner forest problem and the generalized Steiner forest problem. In this problem, we are given a connected graph G = ( V , E ) with non-negative costs c e for the edges e ∈ E , a set of disjoint vertex sets V = { V 1 , V 2 , … , V l } and a parameter k ≤ l . The goal is to find a minimum-cost edge set F ⊆ E that connects at least k vertex sets in V . Our main work is to construct an O ( l ) -approximation algorithm for the k -GSF problem based on a greedy approach and an LP-rounding technique.