Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2022, Volume 204, Pages 37–43
DOI: https://doi.org/10.36535/0233-6723-2022-204-37-43 (Mi into939) 		 
Combinatorial algorithm for finding the number of paths on a directed graph

I. M. Erusalimskyi, M. I. Cherdyntseva

Southern Federal University, Rostov-on-Don
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DOI: https://doi.org/10.36535/0233-6723-2022-204-37-43
Abstract: In this paper, we present an algorithm for finding the number of paths on a directed graph that start at an arbitrary subset of its vertices. The algorithm is based on the ideas underlying the construction of Pascal's triangle. The complexity of the algorithm coincides with the complexity of the well-known Dijkstra algorithm for finding shortest paths on graphs. We also generalize the algorithm proposed to the problem on graphs with reachability constraints.
Keywords: directed graph, path, Pascal's triangle, reachability constraints.
Document Type: Article
UDC: 519.1
MSC: 05C38
Language: Russian
Citation: I. M. Erusalimskyi, M. I. Cherdyntseva, “Combinatorial algorithm for finding the number of paths on a directed graph”, Proceedings of the Voronezh spring mathematical school  "Modern methods of the theory of boundary-value problems. Pontryagin  readings – XXXI". Voronezh, May 3-9, 2020, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 204, VINITI, Moscow, 2022, 37–43
Citation in format AMSBIB
\Bibitem{EruChe22}
\by I.~M.~Erusalimskyi, M.~I.~Cherdyntseva
\paper Combinatorial algorithm for finding the number of paths on a directed graph
\inbook Proceedings of the Voronezh spring mathematical school 
"Modern methods of the theory of boundary-value problems. Pontryagin  readings – XXXI".
Voronezh, May 3-9, 2020
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2022
\vol 204
\pages 37--43
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into939}
\crossref{https://doi.org/10.36535/0233-6723-2022-204-37-43}
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