no. 1
Multiple routing strategies in a labelled network
RAIRO. Operations Research, Tome 35 (2001) no. 1, pp. 85-106

We present here models and algorithms for the construction of efficient path systems, robust to possible variations of the characteristics of the network. We propose some interpretations of these models and proceed to numerical experimentations of the related algorithms. We conclude with a discussion of the way those concepts may be applied to the design of a Public Transportation System.

Keywords: shortest paths, network design, routing 
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     title = {Multiple routing strategies in a labelled network},
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Maublanc, J.; Peyrton, D.; Quilliot, A. Multiple routing strategies in a labelled network. RAIRO. Operations Research, Tome 35 (2001) no. 1, pp. 85-106. https://www.numdam.org/item/RO_2001__35_1_85_0/

[1] F. Bendali and A. Quilliot, Réseaux stochastiques. RAIRO Oper. Res. 24 (1990) 167-190. | Numdam | Zbl | MR | EuDML

[2] T.H. Cormen, C.H. Leiserson and R.L. Rivest, Introduction to algorithms. MIT Press, Cambridge, Mass (1980). | Zbl

[3] E. Dijkstra, A note with two problems in connection with graphs. Numer. Math. I (1959) 269-271. | Zbl | MR | EuDML

[4] R. Dionne and M. Florian, Exact and approximate algorithms for optimal network design. Network 9 (1979) 37-59. | Zbl | MR

[5] A. Farley, Minimum broadcast networks. Networks 10 (1980) 59-70. | Zbl | MR

[6] M. Florian, No linear cost models in transportation analysis. Math. Programming Study 26 (1986) 167-196. | Zbl | MR

[7] P. Fraigniaud and E. Lazard, Methods and problems of communication in usual networks. Discrete Appl. Math. 53 (1994) 79-133. | Zbl | MR

[8] M. Gondran and M. Minoux, Graphes et algorithmes. Ed. Eyrolles (1979). | Zbl | MR

[9] R.M. Karp and J.B. Orlin, Parametric shortest path algorithms with application to cyclic staffing. Discrete Appl. Math. 3 (1981) 37-45. | Zbl | MR

[10] J. Lauriere, Intelligence Artificielle. Eyrolles (1987).

[11] E. Lawler, A procedure for computing the k best solutions to discrete optimization problems and its application to the shortest path problem. Management Sci. 18 (1972) 401-405. | Zbl | MR

[12] E. Minieka, Optimization algorithms for networks and graphs. Marcel Dekker Inc. (1978). | Zbl | MR

[13] M. Minoux, Network synthesis and optimum network design problems: Models, solution methods and applications". Network 19 (1989) 313-360. | Zbl | MR

[14] N. Nilsson, Problem solving methods in A.I. Mac Graw Hill (1971).

[15] A. Quilliot, A retraction problem in graph theory. Discrete Math. 54 (1985) 61-71. | Zbl | MR

[16] A. Quilliot, Algorithmes de cheminements pour des réseaux d'actions à effets non déterministes. Math. Appl. 12 (1991) 25-44. | Zbl

[17] M. Sakarovitch, Chemins, flots, ordonnancements dans les réseaux. Hermann, Paris (1984).

[18] M. Sakarovitch, The k shortest routes and k-shortest chains in a graph. Report ORC, Operation Research Center, University of California, Berkeley (1966) 66-32.

[19] D.R. Shier, On algorithms for finding the k shortest pathes in a network. Networks 9 (1979) 195-214. | Zbl | MR

[20] J. Wardrop, Some theoretical aspects of road traffic research. Proc. Inst. Civil Engrg. II (1952) 325-378.

[21] B. Yaged, Minimum cost routing for dynamic network models. Network 3 (1973) 315-331. | Zbl