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An algorithm for the quickest path problem. (English) Zbl 0881.90124

Summary: The quickest path problem arises when transmitting a given amount of data between two given nodes of a network, a lead time and a capacity (per unit of time) being assigned to each are in the network. In this paper, the problem is regarded as a bicriteria path problem, allowing the use of a very efficient algorithm which solves the quickest path problem for all possible values of the amount of data that has to be transmitted.

MSC:

90C35 Programming involving graphs or networks
90C60 Abstract computational complexity for mathematical programming problems
90B18 Communication networks in operations research
Full Text: DOI

References:

[1] Chen, Y. L.; Chin, Y. H., The quickest path problem, Comput. Oper. Res., 17, 153-161 (1990) · Zbl 0698.90083
[2] Dijkstra, E., A note on two problems in connection with graphs, Numer. Math., 1, 395-412 (1959)
[3] Fredman, M. L.; Tarjan, R. E., Fibonacci heaps and their uses in improved network optimization algorithms, J. Assoc. Comput. Mach., 34, 596-615 (1987) · Zbl 1412.68048
[4] Hansen, P., Bicriterion path problems, (Fandel, G.; Gal, T., Multiple Criteria Decision Making: Theory and Applications. Multiple Criteria Decision Making: Theory and Applications, Lectures Notes in Economics and Mathematical Systems, Vol. 177 (1980), Springer: Springer Cambridge), 109-127 · Zbl 0444.90098
[5] Martins, E. Q.V., On a special class of bicriterion path problems, Eur. J. Oper. Res., 17, 85-94 (1984) · Zbl 0538.90086
[6] Moore, M. H., On the fastest route for convoy-type traffic in flowrate-constrained networks, Transport. Sci., 10, 113-124 (1976)
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