Abstract
The quorumcast routing problem is a generalization of multicasting which arises in many distributed applications. It consists of finding a minimum cost tree that spans the source node and at least q out of m specified nodes on a given undirected weighted graph. In this paper, we solve this problem as a mixed integer program. The experimental results show that our four approaches outperform the state of the art. A sensitivity analysis is also performed on values of q and m.
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References
Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network flows: theory, algorithms, and applications. Prentice-Hall, Inc., Upper Saddle River (1993)
Cordeau, J.-F., Costa, A.M., Laporte, G.: Steiner tree problems with profits. INFOR 44, 99–115 (2006)
Andersen, K.A., Jrnsten, K., Lind, M.: On bicriterion minimal spanning trees: An approximation. Computers and amp; Operations Research 23(12), 1171–1182 (1996)
Applegate, D.L., Bixby, R.E., Chvatal, V., Cook, W.J.: The Traveling Salesman Problem: A Computational Study. Princeton Series in Applied Mathematics. Princeton University Press, Princeton (2007)
Cheung, S.Y., Kumar, A.: Efficient quorumcast routing algorithms. In: Proceedings IEEE INFOCOM 1994, Networking For Global Communications, vol. 2, pp. 840–847 (June 1994)
Chimani, M., Kandyba, M., Ljubić, I., Mutzel, P.: Obtaining optimal k-cardinality trees fast. J. Exp. Algorithmics 14, 5:2.5–5:2.23(2010)
Chopra, S., Tsai, C.Y.: Polyhedral approaches for the steiner tree problem on graphs. In: Du, D.-Z., Cheng, X. (eds.) Steiner Trees in Industries, vol. 11, pp. 175–202. Kluwer Academic Publishers (2001)
Comet. Comet user manual, dynadec (2011), http://dynadec.com/
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. The MIT Press (2009)
Requejo, A.C.C., Agra, A., Santos, E.: Formulations for the weightconstrained minimum spanning tree problem. In: AIP Conf. Proc. vol. 1281, pp. 2166–2169 (2010)
Drexl, M., Irnich, S.: Solving elementary shortest-path problems as mixed-integer programs. OR Spectrum, pp. 1–16 (2012)
Du, B., Gu, J., Tsang, D.H.K., Wang, W.: Quorumcast routing by multispace search. In: Global Telecommunications Conference on Communications: The Key to Global Prosperity, GLOBECOM 1996, vol. 2, pp. 1069–1073 (November 1996)
Fujie, T.: The maximum-leaf spanning tree problem: Formulations and facets. Networks 43(4), 212–223 (2004)
Garey, M.R., Johnson, D.S.: Computers and Intractability; A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1990)
Goemans, M.X., Myung, Y.-S.: A catalog of steiner tree formulations. Networks 23(1), 19–28 (1993)
S.T. Henn.: Weight-Constrained Minimum Spanning Tree Problem. PhD thesis, University of Kaiserslautern (2007)
Ibrahim, M.S., Maculan, N., Minoux, M.: A strong flow-based formulation for the shortest path problem in digraphs with negative cycles. International Transactions in Operational Research 16(3), 361–369 (2009)
Wayne, K.: Union-find algorithms. (2008), http://www.cs.princeton.edu/r~s/AlgsDS07/01UnionFind.pdf
Koch, T., Martin, A.: Solving steiner tree problems in graphs to optimality. Networks 32, 207–232 (1998)
Koch, T., Martin, A., Voß, S.: SteinLib: An updated library on steiner tree problems in graphs. Technical Report ZIB-Report 00-37, Konrad-Zuse-Zentrum für Informationstechnik Berlin, Takustr. 7, Berlin (2000)
Kulkarni, R.V., Bhave, P.R.: Integer programming formulations of vehicle routing problems. European Journal of Operational Research 20(1), 58–67 (1985)
Ljubi, 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. Mathematical Programming 105, 427–449 (2006)
Ljubi, 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. In: Mathematical Progamming. Series B (2006)
Low, C.P.: A fast search algorithm for the quorumcast routing problem. Inf. Process. Lett. 66(2), 87–92 (1998)
Lucena, A., Beasley, J.E.: A branch and cut algorithm for the steiner problem in graphs. Networks 31, 39–59 (1998)
Lucena, A., Maculan, N., Simonetti, L.: Reformulations and solution algorithms for the maximum leaf spanning tree problem. Computational Management Science 7, 289–311 (2010)
Magnanti, T.L., Wolsey, L.A.: Optimal trees. In: Monma, C.L., Ball, M.O., Magnanti, T.L., Nemhauser, G.L. (eds.) Network Models. Handbooks in Operations Research and Management Science, vol. 7, ch. 9, pp. 503–615. Elsevier (1995)
Miller, C.E., Tucker, A.W., Zemlin, R.A.: Integer programming formulation of traveling salesman problems. J. ACM 7(4), 326–329 (1960)
Pham, Q., Deville, Y.: Solving the quorumcast routing problem by constraint programming. Constraints 17, 409–431 (2012)
G. Skorobohatyj.: Finding a minimum cut between all pairs of nodes in an undirected graph (2008), http://elib.zib.de/pub/Packages/mathprog/mincut/all-pairs/index.html
Uchoa, E.: Reduction tests for the prize-collecting steiner problem. Operations Research Letters 34(4), 437–444 (2006)
Wang, B., Hou, J.C.: An efficient QoS routing algorithm for quorumcast communication. Computer Networks Journal 44(1), 43–61 (2004)
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Bui, Q.T., Pham, Q.D., Deville, Y. (2014). Solving the Quorumcast Routing Problem as a Mixed Integer Program. In: Simonis, H. (eds) Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2014. Lecture Notes in Computer Science, vol 8451. Springer, Cham. https://doi.org/10.1007/978-3-319-07046-9_4
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