Abstract
The basic problem considered here is that of find ing the “best path” of infinite length in a directed graph with a finite number of vertices. “Best path” is interpreted to mean that path which minimizes a suitable sum of costs, when a cost is assigned to each arc.
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References
I.L. Traiger and A. Gill, “On an Asymptotic Problem in Finite Directed, Weighted Graphs; Information and Control, Volume 13, 6, December 1968, pp. 527–533.
G.B. Dantzig, “All Shortest Routes in a Graph”, Teorie des Graphes, International Symposium, Rome, Italy, Dunod, Paris, 1966.
G.B. Dantzig, W.O. Blattner, M.R. Rao, “Finding a Cycle in a Graph with Minimum Cost to Time Ratio with Application to a Ship Routing Problem’, ibid.
E.L. Lawler, ’`Optimal Cycles in Doubly Weighted Directed Linear Graphs“, ibid.
S. Rinaldi, ’’Asymptotic Properties of the Cost Functions Associated to any Infinite Path in a Finite Graph, Technical Report No 69–8, Operations Research House, Stanford University, Stanford, California, September 1968.
A. Gill and I.L. Traiger, ‘Computation of Optimal Paths in Finite Graphs“, Computation Methods in Optimization Problems -2, Academic Press, New-York, 1969.
P. Dorato, “Steady-State Optimal Control of Finite-State Machines”, Automatica, Volume 7, 1971, pp. 351–358.
R. Bellman, K.L. Cooke and J.A. Lockett, ’’Algorithms, Graphs, and Computers’’, Academic Press, New-York 1970.
A. Kaufman and R. Gruon, ‘Dynamic Programming“, Academic Press, New-York, 1967.
T.M. Apostal, “Mathematical Analysis” Addison-Wesley Pub. Co., Inc., Reading, Massachusset, U.S.A., 1957.
R. Howard, ‘Dynamic Programming and Markov Process Technology Press, M.I.T., J. Wiley and Sons, Inc., New-York, 1960.
J. Shapiro, “Shortest Route Methods for Finite State Space Deterministic Dynamic Programming Problems”, SIAM Jour. Appl. Math., vol. 16, n° 6, November 1968, pp. 1232–1254.
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© 1972 Springer-Verlag Wien
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Dorato, P. (1972). Asymptotic Optimization in Finite Directed Graphs. 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_2
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DOI: https://doi.org/10.1007/978-3-7091-2652-3_2
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