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.
We are deeply thankful to Christina Backes from the Department of Human Genetics, Saarland University, who helped in the understanding and interpretation of the regulatory network instances considered in this paper. This research is partially conducted during the research stay of Ivana Ljubić at the TU Dortmund, supported by the APART Fellowship of the Austrian Academy of Sciences. This support is greatly acknowledged. Eduardo Álvarez-Miranda thanks the Institute of Advanced Studies of the Università di Bologna from where he is a Ph.D. Fellow.
- 1.Backes, C., Rurainski, A., Klau, G., Müller, O., Stöckel, D., Gerasch, A., Küntzer, J., Maisel, D., Ludwig, N., Hein, M., Keller, A., Burtscher, H., Kaufmann, M., Meese, E., Lenhof, H.: An integer linear programming approach for finding deregulated subgraphs in regulatory networks. Nucleic Acids Res. 1, 1–13 (2011) Google Scholar
- 2.Bateni, M., Chekuri, C., Ene, A., Hajiaghayi, M., Korula, N., Marx, D.: Prize-collecting Steiner problems on planar graphs. In: Randall, D. (ed.) Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011, San Francisco, CA, USA, January 23–25, pp. 1028–1049 (2011) Google Scholar
- 7.Dilkina, B., Gomes, C.: Solving connected subgraph problems in wildlife conservation. In: Lodi, A., Milano, M., Toth, P. (eds.) CPAIOR. LNCS, vol. 6140, pp. 102–116. Springer, Berlin (2010) Google Scholar
- 12.genetrail.bioinf.uni-sb.de/ilp/. Accessed 10 September 2012
- 18.Hochbaum, D.S., Pathria, A.: Node-optimal connected k-subgraphs. Manuscript, UC Berkeley (1994) Google Scholar
- 20.Johnson, D.S., Minkoff, M., Phillips, S.: The prize-collecting Steiner tree problem: theory and practice. In: Proceedings of the 11th ACM-SIAM Symposium on Discrete Algorithms, SODA 2000, San Francisco, CA, USA, 9–11 January, pp. 760–769 (2000) Google Scholar
- 25.www.planet-lisa.net/. Accessed 10 September 2012
- 26.Yamamoto, T., Bannai, H., Nagasaki, M., Miyano, S.: Better decomposition heuristics for the maximum-weight connected graph problem using betweenness centrality. In: Gama, J., Costa, V., Jorge, A., Brazdil, P. (eds.) Discovery Science. LNCS, vol. 5808, pp. 465–472. Springer, Berlin (2009) CrossRefGoogle Scholar