Geodesic
Extreme paths on graphs with simultaneously varying arc durations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 225 (2023), pp. 69-72

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In this paper, we propose an algorithm for finding the fastest path on a graph with two weights on each arc, namely, the times required to pass the arc before the beginning of rush hour and during rush hours, if the time of the beginning of rush hours is also indicated. The algorithm proposed can be considered a modification of the classical E. Dijkstra algorithm.
Keywords: weighted graph, arc weight, shortest time path, Dijkstra's algorithm, rush hour. 
@article{INTO_2023_225_a5,
     author = {I. M. Erusalimskyi and M. I. Osipov and V. A. Skorokhodov},
     title = {Extreme paths on graphs with simultaneously varying arc durations},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {69--72},
     publisher = {mathdoc},
     volume = {225},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_225_a5/}
}
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I. M. Erusalimskyi; M. I. Osipov; V. A. Skorokhodov. Extreme paths on graphs with simultaneously varying arc durations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 225 (2023), pp. 69-72. http://geodesic.mathdoc.fr/item/INTO_2023_225_a5/