Finding a contour with the smallest mean expenses in a graph with variable lengths of arcs. The simplest case

Authors

  • Joseph V. Romanovsky St.Petersburg State University, Universitetskaya nab., 7-9, St.Petersburg, 199034, Russian Federation;

Abstract

Consider a problem: find a contour with minimal ratio of total expenses to total length in an oriented graph when each its arc is associated with two values: its expanses and its length. The simplest case is when the graph consistes of a contour and it is required to select the lengths of the arcs. Two partial cases were considered: a) a discrete set of possibilities for each arc and b) the dependence: cost = a+b ·length^2. Refs 19. Figs 1.

Keywords:

optimal control, Bellman equation, contour with minimal expenses, tropical mathematics

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Published

2014-11-01

How to Cite

Romanovsky, J. V. (2014). Finding a contour with the smallest mean expenses in a graph with variable lengths of arcs. The simplest case. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 1(4), 571–578. Retrieved from https://math-mech-astr-journal.spbu.ru/article/view/11090

Issue

Vol. 1 No. 4 (2014)

Section

Mathematics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.