Abstract
Minimum Spanning Trees (MSTs) are ubiquitous in optimization problems in networks. Even though fast algorithms exist to solve the MST problem, real world applications are usually subject to constraints that do not let us apply such methods directly. In these cases we confront a version of the MST called the “Weighted Spanning Tree” (WST) in which we look for a spanning tree in a graph that satisfies other side constraints and is of minimum cost. In this paper we implement this constraint using a lower bound and learning to accelerate the search and thus reduce the solving time. We show that having this propagator is tremendously beneficial for solvers and we show the benefits of learning.
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References
Achuthan, N., Caccetta, L., Caccetta, P., Geelen, J.: Algorithms for the minimum weight spanning tree with bounded diameter problem. Optim. Tech. Appl. 1(2), 297–304 (1992)
Akgün, İ., Tansel, B.Ç.: Min-degree constrained minimum spanning tree problem: new formulation via miller-tucker-zemlin constraints. Comput. Oper. Res. 37(1), 72–82 (2010)
Bala, K., Petropoulos, K., Stern, T.E.: Multicasting in a linear lightwave network. In: Proceedings of the Twelfth Annual Joint Conference of the IEEE Computer and Communications Societies, Networking: Foundation for the Future, IEEE, INFOCOM 1993, pp. 1350–1358. IEEE (1993)
Bookstein, A., Klein, S.T.: Compression of correlated bit-vectors. Inf. Syst. 16(4), 387–400 (1991)
Chandy, K.M., Lo, T.: The capacitated minimum spanning tree. Networks 3(2), 173–181 (1973)
Chu, G., Stuckey, P.J.: Dominance breaking constraints. Constraints 20(2), 155–182 (2015)
Chu, G.G.: Improving combinatorial optimization. Ph.D. thesis, The University of Melbourne (2011)
Dooms, G., Katriel, I.: The minimum spanning tree constraint. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 152–166. Springer, Heidelberg (2006)
Dooms, G., Katriel, I.: The “not-too-heavy spanning tree” constraint. In: Van Hentenryck, P., Wolsey, L.A. (eds.) CPAIOR 2007. LNCS, vol. 4510, pp. 59–70. Springer, Heidelberg (2007)
Gruber, M., Raidl, G.R.: A new 0–1 ILP approach for the bounded diameter minimum spanning tree problem. In: Gouveia, L., Mourão, C. (eds.) Proceedings of the 2nd International Network Optimization Conference 2005, Lisbon, Portugal, vol. 1, pp. 178–185 (2005). https://www.ac.tuwien.ac.at/files/pub/gruber-05.pdf
Gruber, M., Raidl, G.R.: Variable neighborhood search for the bounded diameter minimum spanning tree problem. In: Hansen, P., Mladenovi, N., Pérez, J.A.M., Batista, B.M., Moreno-Vega, J.M. (eds.) Proceedings of the 18th MiniEuro Conference on Variable Neighborhood Search, Tenerife, Spain (2005). https://www.ac.tuwien.ac.at/files/pub/gruber-05a.pdf
Gruber, M., Raidl, G.R.: (Meta-)Heuristic separation of jump cuts in a branch & cut approach for the bounded diameter minimum spanning tree problem. In: Maniezzo, V., Stützle, T., Voß, S. (eds.) Hybridizing Metaheuristics and Mathematical Programming. Annals of Information Systems, vol. 10, pp. 209–229. Springer, Heidelberg (2010)
Klein, A., Haugland, D., Bauer, J., Mommer, M.: An integer programming model for branching cable layouts in offshore wind farms. In: An Le Thi, H., Dinh, T.P., Nguyen, N.T. (eds.) Modelling, Computation and Optimization in Information Systems and Management Sciences, pp. 27–36. Springer, Switzerland (2015)
Narula, S.C., Ho, C.A.: Degree-constrained minimum spanning tree. Comput. Oper. Res. 7(4), 239–249 (1980)
Noronha, T.F., Ribeiro, C.C., Santos, A.C.: Solving diameter-constrained minimum spanning tree problems by constraint programming. Int. Trans. Oper. Res. 17(5), 653–665 (2010)
Ohrimenko, O., Stuckey, P., Codish, M.: Propagation via lazy clause generation. Constraints 14(3), 357–391 (2009). http://dx.doi.org/10.1007/s10601-008-9064-x
Papadimitriou, C.H., Vazirani, U.V.: On two geometric problems related to the travelling salesman problem. J. Algorithms 5(2), 231–246 (1984)
Prud’homme, C., Fages, J.G., Lorca, X.: Choco3 Documentation. TASC, INRIARennes, LINA CNRS UMR 6241, COSLING S.A.S (2014). http://www.choco-solver.org
Ravi, R., Goemans, M.: The constrained minimum spanning tree problem. Algorithm Theory SWAT 1996, pp. 66–75 (1996)
Raymond, K.: A tree-based algorithm for distributed mutual exclusion. ACM Trans. Comput. Syst. (TOCS) 7(1), 61–77 (1989)
Régin, J.-C.: Simpler and incremental consistency checking and arc consistency filtering algorithms for the weighted spanning tree constraint. In: Trick, M.A. (ed.) CPAIOR 2008. LNCS, vol. 5015, pp. 233–247. Springer, Heidelberg (2008)
Régin, J.-C., Rousseau, L.-M., Rueher, M., van Hoeve, W.-J.: The weighted spanning tree constraint revisited. In: Lodi, A., Milano, M., Toth, P. (eds.) CPAIOR 2010. LNCS, vol. 6140, pp. 287–291. Springer, Heidelberg (2010)
dos Santos, A.C., Lucena, A., Ribeiro, C.C.: Solving diameter constrained minimum spanning tree problems in dense graphs. In: Ribeiro, C.C., Martins, S.L. (eds.) WEA 2004. LNCS, vol. 3059, pp. 458–467. Springer, Heidelberg (2004)
de Uña, D.: Weighted spanning tree benchmarks (2015). http://people.eng.unimelb.edu.au/pstuckey/wst/
de Uña, D., Gange, G., Schachte, P., Stuckey, P.J.: Steiner tree problems with side constraints using constraint programming. In: Proceedings of the Thertieth AAAI Conference on Artificial Intelligence. AAAI Press (2016)
Wang, S., Lang, S.: A tree-based distributed algorithm for the k-entry critical section problem. In: International Conference on Parallel and Distributed Systems, 1994, pp. 592–597. IEEE (1994)
Acknowledgement
Diego de Uña thanks “la Caixa” Foundation for partially funding his Ph.D. studies at The University of Melbourne.
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de Uña, D., Gange, G., Schachte, P., Stuckey, P.J. (2016). Weighted Spanning Tree Constraint with Explanations. In: Quimper, CG. (eds) Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2016. Lecture Notes in Computer Science(), vol 9676. Springer, Cham. https://doi.org/10.1007/978-3-319-33954-2_8
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