Abstract
We discuss fast exponential time exact algorithms for generalized combinatorial optimization problems. The list of discussed NP-complete generalized combinatorial optimization problems includes the generalized minimum spanning tree problem, the generalized subset assignment problem and the generalized travelling salesman problem.
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References
Dror, M., Haouari, M.: Generalized Steiner Problems and Other Variants. Journal of Combinatorial Optimization 4, 415–436 (2000)
Dror, M., Haouari, M., Chaouachi, J.: Generalized Spanning Trees. European Journal of Operational Research 120, 583–592 (2000)
Feremans, C.: Generalized Spanning Trees and Extensions, PhD thesis, Universite Libre de Bruxelles, Belgium (2001)
Feremans, C., Labbe, M., Laporte, G.: A Comparative Analysis of Several Formulations of the Generalized Minimum Spanning Tree Problem. Networks 39(1), 29–34 (2002)
Fischetti, M., Salazar, J.J., Toth, P.: The symmetric generalized traveling salesman polytope. Networks 26, 113–123 (1995)
Fischetti, M., Salazar, J.J., Toth, P.: A branch-and-cut algorithm for the symmetric generalized traveling salesman problem. Operations Research 45, 378–394 (1997)
Fisher, M.L., Jaikumar, R., van Wassenhove, L.N.: A multiplier adjustment method for generalized assignment problem. Management Science 32/9, 1095–1103 (1986)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A guide to the theory of NP-Completeness. Freeman, San Francisco, California (1979)
Kuhn, H.W.: The hungarian method for the assignment problem. Naval Research Logistic Quarterly 2, 83–97 (1955)
Laporte, G., Asef-Vaziri, A., Sriskandarajah, C.: Some applications of the generalized traveling salesman problem. J. Oper. Res. Soc. 47, 1461–1467 (1996)
Laporte, G., Nobert, Y.: Generalized Traveling Salesman through n sets of nodes: an integer programming approach. INFOR 21, 61–75 (1983)
Noon, C.E., Bean, J.C.: A Lagrangian based approach for the asymmetric generalized traveling salesman problem. Operations Research 39, 623–632 (1991)
Myung, Y.S., Lee, C.H., Tcha, D.w.: On the Generalized Minimum Spanning Tree Problem. Networks 26, 231–241 (1995)
Pop, P.C.: The Generalized Minimum Spanning Tree Problem, PhD thesis, University of Twente, The Netherlands (2002)
Pop, P.C.: New Models of the Generalized Minimum Spanning Tree Problem. Journal of Mathematical Modelling and Algorithms 3(2), 153–166 (2004)
Pop, P.C.: On the Prize-Collecting Generalized Minimum Spanning Tree Problem. In Annals of Operations Research (to appear)
Pop, P.C., Kern, W., Still, G.: Approximation Theory in Combinatorial Optimization. Application to the Generalized Minimum Spanning Tree Problem, Revue d’Analyse Numerique et de Theorie de l’Approximation, Tome, vol. 34(1), pp. 93–102 (2005)
Pop, P.C., Kern, W., Still, G.: A New Relaxation Method for the Generalized Minimum Spanning Tree Problem. European Journal of Operational Research 170, 900–908 (2006)
Yannakakis, M.: Expressing combinatorial optimization problems by linear programs. Journal of Computer and System Sciences 43, 441–466 (1991)
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Pop, P.C., Pop Sitar, C., Zelina, I., Taşcu, I. (2007). Exact Algorithms for Generalized Combinatorial Optimization Problems. In: Dress, A., Xu, Y., Zhu, B. (eds) Combinatorial Optimization and Applications. COCOA 2007. Lecture Notes in Computer Science, vol 4616. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73556-4_18
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DOI: https://doi.org/10.1007/978-3-540-73556-4_18
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