Abstract
The object of the paper is the study of graph problems involving paths or routing.
As a result of the introduction of a very general algebraic structure, most of these problems will be unified into a common presentation. Moreover it will generalize the results of authors having investigated this topic and thus solve a few new problems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bellman R., “On a routing problem”, Quart. Appl. Math., 16 (1958:
Benzaken C., “Structures algébriques des cheminements: pseudotreillis, gerbier de carré nul”, in Network an Switching Theory, edited by G. Biorci, Academic Press, 1968, p. 40–47.
Carre B.A., “An algebra for network routing problems”, J. Inst. Maths. Applics, 7 (1971), p. 273–294.
Dantzig G.B., “All shortest routes in a graph”, Proc. I.C.C. Conference on Theory of Graphs, Rome (1966), Gordon and Breach, N.Y., p. 91–92.
Floyd R.W., “Algorithm 97: Shortest path”, Communication of ACM, Vol. 5 (1962) p. 345.
Ford L.R. and Fulkerson D.R., “Flows in Network”, Princeton University Press, 1962.
Gondran M., “Algèbre linéaire et cheminement dans un graphe”, R.A.I.R.O., 8ième année, V-3, 1974.
Gondran M., “Démonstration de la convergence des algorithmes de Gauss-Jordan généralisé et “escalier” généralisé, note EDF à paraître.
Minieka E., “On computing Sets of Shortest Paths in a graph”, Communications of the ACM, June 1974, V. 17, 6, p. 351–3.
Minieka E. and Shier D.R., “A note on an algebra for the k best routes in a network”, J. Inst. Math. Appl. 11, 1973, p. 145–149.
Müller — Merbach H., “Die Inversion von Gozinto-Matrizen mit einem Graphen-Orientierten Verfahren, Elektroniche Daten Verarbeitung 11, 1969, P. 310–314
Peteanu V., “An algebra of the optimal path in networks”, Mathematica, Vol. 9 (1967), n°2, p. 335–342.
Pichat E., “Algorithms for finding the maximal elements of a finite universal algebra”, Proc. IFIP Congress 1968, EDINBURG, Booklet A, p. 96–101.
Robert P. and Ferland J., “Genéralisation de l’algorithme de WARSHALL”, Rev. Française Informatique et R.O. (1968) n° 7, p. 71–85.
Roy B., “Transitivité et connexité”, C.R. Acad. Sciences Paris, Tome 249 (1959), p.216.
Roy B., “Chemins et circuits, enumeration et optimisation: procédures algébriques”, this book.
Shier D.R., “A decomposition algorithm for optimality problems in tree-structured networks”, Discrete Mathematics 6, 1973, p. 175–189
Warshall S., “A theorem on boolean Matrices”, J. of ACM, vol. 9 (1962), p. 11–12.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1975 D. Reidel Publishing Company, Dordrecht-Holland
About this paper
Cite this paper
Gondran, M. (1975). Path Algebra and Algorithms. In: Roy, B. (eds) Combinatorial Programming: Methods and Applications. NATO Advanced Study Institutes Series, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-7557-9_6
Download citation
DOI: https://doi.org/10.1007/978-94-011-7557-9_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-011-7559-3
Online ISBN: 978-94-011-7557-9
eBook Packages: Springer Book Archive