Some generalizations of the steiner problem in graphs

The Steiner Problem in Graphs (SP) is the problem of finding a set of edges with minimum total weight which connects a given subset of nodes in an edge‐weighted (undirected) graph. In the more general Node‐weighted Steiner Problem (NSP) also node weights are considered. A restricted minimum spanning tree model is adjusted for the NSP as well as for the Steiner Forest Problem, a newly introduced generalization. The NSP is related to the Directed Steiner Problem. Reduction tests for the SP, reducing the size of the problem graph, are adapted for these generalizations and some new tests are developed.