Abstract
In this chapter, we wish to treat two discrete optimization problems. However, we shall not conceal that only a small insight into the solution methods can be given, since today there already exist such a variety of different methods and algorithms based on them for solving especially the travelling salesman problem that it is impossible at present to make a final evaluation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Eastman, W. L.: A solution to the Traveling Salesman Problem, American Summer Meeting of the Econometric Society, Cambridge, Mass., August 1958.
Finkel’štejn, Ju. Ju.: Näherungsverfahren und Anwendungsprobleme der diskreten Optimierung (Russian), Moscow 1976.
Korbut, A. A., und J. J. Finkelstein: Diskrete Optimierung, Berlin 1971. (Translated from Russian.)
Hansen, K. H., and J. Krarup: Improvements of the Held-Karp-algorithm for the symmetric Traveling Salesman Problem, Math. Progr. 7 (1974), 87–96.
Held, M., and R. M. Karp: The Traveling Salesman Problem and minimum spanning trees, Operations Res. 18 (1970), 1138–1162.
Held, M., and R. M. Karp: The Traveling Salesman Problem and minimum spanning trees II, Math. Progr. 1 (1971), 6–25.
Little, J., K. Murty, D. Sweeney and C. Karel: An algorithm for the Traveling Salesman Problem, Operations Res. 11 (1963), 972–989.
Mitten, L. G.: Branch-and-bound methods: General formulation and properties, Operations Res. 18 (1970), 24–34.
Noltemeier, H.: Graphentheorie mit Algorithmen und Anwendungen, Berlin/New York 1976.
Piehler, J.: Ein Beitrag zum Reihenfolgeproblem, Unternehmensforschung 4 (1960), 138–142.
Sachs, H.: Theorie der endlichen Graphen, Teil I, Leipzig 1970.
Schoch, M.: Das Erweiterungsprinzip und seine Anwendung, Berlin and Munich/ Vienna 1976.
Sciffart, E.: Über Lösungsmethoden einiger Reihenfolgeprobleme, Wiss. Z. TH Magdeburg 9 (1965), 1–5.
Späth, H.: Ausgewählte Operations-Research-Algorithmen in FORTRAN, Munich/ Vienna 1975.
Steckhan, H., und R. Thome: Vereinfachungen der Eastmanschen Branch-and-Bound-Lösung für symmetrische Traveling Salesman Probleme, in: Operations-Res. Verfahren Bd. XIV. Meisenheim 1972, p. 361-389.
Thompson, G. L.: Algorithmic and computational methods for solving symmetric and asymmetric traveling salesman problems, in: Workshop in Integer Programming, Bonn 1975 (in print).
Tinhofer, G.: Methoden der Angewandten Graphentheorie, Vienna/New York 1976.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1984 VEB Deutscher Verlag der Wissenschaften, Berlin
About this chapter
Cite this chapter
Walther, H. (1984). The assignment and the travelling salesman problems. In: Ten Applications of Graph Theory. Mathematics and Its Applications, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7154-7_7
Download citation
DOI: https://doi.org/10.1007/978-94-009-7154-7_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-7156-1
Online ISBN: 978-94-009-7154-7
eBook Packages: Springer Book Archive