The Maximum Weight Connected Subgraph Problem

The Maximum (Node-) Weight Connected Subgraph Problem (MWCS) searches for a connected subgraph with maximum total weight in a node-weighted (di)graph. In this work we introduce a new integer linear programming formulation built on node variables only, which uses new constraints based on node-separators. We theoretically compare its strength to previously used MIP models in the literature and study the connected subgraph polytope associated with our new formulation. In our computational study we compare branch-and-cut implementations of the new model with two models recently proposed in the literature: one of them using the transformation into the Prize-Collecting Steiner Tree problem, and the other one working on the space of node variables only. The obtained results indicate that the new formulation outperforms the previous ones in terms of the running time and in terms of the stability with respect to variations of node weights.