The quest for optimal/stable paths in graphs concerns a few practical or theoretical areas. Taking part in the quest, this paper adopts an abstract, general, equilibrium-oriented approach: it uses (quasi-arbitrary) arc-labelled digraphs, and assumes little about the structure of the sought paths and the definition of equilibrium, i.e. optimality/stability. The paper gives both a sufficient condition and a necessary condition for equilibrium existence for every "graph", pinpoints the difference between these conditions, and shows coincidence when optimality relates to a total order. These results are applied to network routing. © 2008 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Le Roux, S. (2008). Graphs and path equilibria. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5034 LNCS, pp. 247–258). Springer Verlag. https://doi.org/10.1007/978-3-540-68880-8_24
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