Abstract
The problem of finding a shortest elementary (*) cycle spanning all the nodes of a given arc weighted graph is called traveling salesman problem (TSP) and any solution is called a shortest hamiltonian cycle (SH) or a shortest tour of the given graph.
Partially supported by Centro di Telecomunicazioni Spaziali (CNR) of Milano, Italy
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
M. Bellmore and G.L. Nemhauser, “The traveling salesman problem: a survey’ Oper. Res. 16, N°3 (1968) 538–558.
A.M. Isaac and E. Turban, ’’’Some comments on the traveling salesman problem’, Oper. Res. 17, N°3 (1969) 543–546.
P.C. Gilmore and R.E. Gomory, “Sequencing a one-state variable machine: a solvable case of the travel ing salesman problem’ Oper. Res. 12 (1964) 655–679.
E.L. Lawler, “A solvable case of the traveling salesman problem” Math. Progr. 1, N° 2 (1971) 267–269.
M. Held and R.M. Karp, ‘The traveling salesman problem and minimum spanning trees’’, Oper. Res. 18 (1970).
M. Held and R.M. Karp, “The traveling salesman problem and minimum spanning tree: part II, Math. Progr. 1 (1971), 6–25.
P. Krolak and W. Felts, “A man-machine approach toward solving the traveling salesman problem” Comm. ACM 14, N° 5 (1971) 327–334.
N. Chirstofides, ‘The shortest Hamiltonian Chain of a Graph’, SIAM J. Appl. Math. 19, N° 4 (1970) 689–696.
A.G. Azpeitia and D. Riley, “ The longest path in a network”, J. Math. An. and Appl. 30 (1970) 636638.
P.E. Hart, N.L. Nillson and B. Raphael, “ A formal basis for the heuristic determination of minimum cost paths” IEEE Trans. on SSC,SSC-4 N° 2 (1968) 100–107.
L. Fratta and F. Maffioli, “ On the shortest Hamiltonian chain of a network’, 2nd International Symp. on Network Theory, Herceg-Novi (YU) July 1972.
P.M. Camerini, L. Fratta, F. Maffioli, “A Heuristically guided Algorithm for the Travelling Salesman Problem”, (to be published).
K. Steiglits and P. Weiner, “ Some improved algorithms for computer solution of the traveling sales man problem” Proc. 6th Allerton Conference on Circuits and System Theory (1968) 814–821.
E.L. Lawler, “The complexity of combinatorial computa tions: a survey”, Proc. 1971 Polytechnic Institute of Brooklyn Symp. on Computers and Automata.
N. Deo and S.L. Hakimi, “ The shortest generalized Hamiltonian tree” Proc. 3rd Allerton Conference on Circuits and System Theory (1965), 879–883.
Comm. of ACM vol. 15, N° 4 (1972) 273–274.
G.B. Dantzig, “Linear Programming and Extensions”, Princeton U. Press 1963, 361–366.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1972 Springer-Verlag Wien
About this chapter
Cite this chapter
Maffioli, F. (1972). Optimal Hamiltonian Cycles: A Survey of Recent Results. In: Marzollo, A. (eds) Periodic Optimization. International Centre for Mechanical Sciences, vol 135. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2652-3_5
Download citation
DOI: https://doi.org/10.1007/978-3-7091-2652-3_5
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-81135-1
Online ISBN: 978-3-7091-2652-3
eBook Packages: Springer Book Archive