"... Abstract. Moss and Rabani  study constrained node-weighted Steiner tree problems with two independent weight values associated with each node, namely, cost and prize (or penalty). They give an O(logn)-approximation algorithm for the prize-collecting node-weighted Steiner tree problem (PCST)—wher ..."
"... given a graph with costs/weights on edges and/or nodes and prescribed connectivity require-ments/demands. Among the subgraphs of G that satisfy the requirements, we seek to find one of minimum cost. Formally, the problem is defined as follows. Given a graph G = (V,E) and Q ⊆ V, the Q-connectivity λQ ..."