Abstract
The prize-collecting Steiner tree (PCST) problem is a broadly studied problem in combinatorial optimization. It has been used to model several real world problems related to utility networks. More recently, researchers have started using PCSTs to study biological networks. Biological networks are typically very large in size. This can create a considerable challenge for the available PCST solving methods. Taking this fact into account, we have developed methods for the PCST that efficiently scale up to large biological network instances. Namely, we have devised a heuristic method based on the Minimum Spanning Tree and a matheuristic method composed of a heuristic clustering phase and a solution phase. In this work, we provide a performance comparison for these methods by testing them on large gene interaction networks. Experimental results are reported for the methods, including running times and objective values of the solutions.
This is a preview of subscription content, log in via an institution to check access.
Notes
References
Johnson, D.S., Minkoff, M., Phillips, S.: The prize collecting Steiner tree problem: theory and practice. In: Proceedings of 11th ACM–SIAM Symposium on Discrete Algorithms, pp. 760–769 (2000)
Bechet, M.B., Borgs, C., Braunsteinc, A., Chayes, J., Dagkessamanskaia, A., François, J.M., Zecchina, R.: Finding undetected protein associations in cell signalling by belief propagation. PNAS 108, 882–887 (2010)
Bienstock, D., Goemans, M.X., Simchi-Levi, D., Williamson, D.: A note on the prize collecting traveling salesman problem. Math. Progr. 59, 413–420 (1993)
Segev, A.: The node-weighted Steiner tree problem. Networks 17, 1–17 (1987)
Ljubic, I., Weiskircher, R., Pferschy, U., Klau, G.W., Mutzel, P., Fischetti, M.: An algorithmic framework for the exact solution of the prize\(-\)collecting Steiner tree problem. Math. Progr. 105(2), 427–449 (2006)
Ljubic, I., Weiskircher, R., Pferschy, U., Klau, G., Mutzel, P., Fischetti, M.: Solving the prize\(-\)collecting Steiner tree problem to optimality. Proceedings of ALENEX, Seventh Workshop on Algorithm Engineering and Experiments, pp. 68–76 (2005)
Canuto, S.A., Resende, M.G.C., Ribeiro, C.C.: Local search with perturbation for the prize- collecting Steiner tree problem in graphs. Networks 38, 50–58 (2001)
Klau, G.W., Ljubic, I., Moser, A., Mutzel, P., Neuner, P., Pferschy, U., Raidl, G., Weiskircher, R.: Combining a memetic algorithm with integer programming to solve the prize-collecting Steiner tree problem. Genet. Evol. Comput. GECCO 2004(3102), 1304–1315 (2004)
Tuncbag, N., McCallum, S., Huang, S.C., Fraenkel, E.: SteinerNet: a web server for integrating omic data to discover hidden components of response pathways. Nucl. Acids Res. 1–5 (2012)
Dittrich, M.T., Klau, G.W., Rosenwald, A., Dandekar, T., Mueller, T.: Identifying functional modules in protein-protein interaction networks: an integrated exact approach. Bioinformatics 26, 223–231 (2008)
Beisser, D., Klau, G.W., Dandekar, T., Mueller, T.: T, and M. Dittrich. BioNet: an R-package for the functional analysis of biological networks. Bioinformatics 26(8), 1129–1130 (2010)
Akhmedov, M., Kwee, I., Montemanni, R.: A fast heuristic for the prize-collecting steiner tree problem. Lect. Notes Manag. Sci. 6, 207–216 (2014)
Akhmedov, M., Kwee, I., Montemanni, R.: A divide and conquer matheuristic algorithm for the prize-collecting Steiner tree problem. Computers and Operation Research (to appear)
Margolin, A.A., Nemenman, I., Basso, K., Wiggins, C., Stolovitzky, G., Favera, R.D., Califano, A.: Aracne: an algorithm for the reconstruction of gene regulatory networks in a mammalian cellular context. BMC Bioinform. 7(Suppl 1), S7 (2006)
Acknowledgements
M. Akhmedov is supported by Swiss National Science Foundation through project 205321-147138/1: “Steiner Trees for Functional Analysis in Cancer System Biology”.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing Switzerland
About this paper
Cite this paper
Akhmedov, M., Kwee, I., Montemanni, R. (2017). A Comparison of Heuristic Methods for the Prize-Collecting Steiner Tree Problem and Their Application in Genomics. In: Dörner, K., Ljubic, I., Pflug, G., Tragler, G. (eds) Operations Research Proceedings 2015. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-42902-1_14
Download citation
DOI: https://doi.org/10.1007/978-3-319-42902-1_14
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-42901-4
Online ISBN: 978-3-319-42902-1
eBook Packages: Business and ManagementBusiness and Management (R0)