Summary
This paper presents an algorithm for finding all shortest distances in a network with a large number of strongly connected components. If the network hasN nodes the number of computations required by this algorithm is asymptotically 1/6N(N−1) (N−2) tripel operations.
Zusammenfassung
In der vorliegenden Arbeit wird ein Algorithmus zur Bestimmung der Längen aller kürzesten Wege in Netzwerken mit mehreren strengen Zusammenhangskomponenten entwickelt. Besitzt das NetzwerkN Knoten, so hat man bei diesem Algorithmus asymptotisch insgesamt 1/6N(N−1 (N−2) Additionen und ebenso viele Vergleiche durchzuführen.
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References
Floyd, R. W.: Algorithm 97: Shortest Path, Communication of ACM6, 345, 1962.
Hu, T. C.: Decomposition Algorithm for Shortest Paths in a Network, J. ORSA16, 91–102, 1968.
—: Integer Programming and Networks Flows, Addison-Wesley, Reading, Massachusetts 1970.
Knuth, D. E.: The Art of Computer Programming, Vol. 1, Addison-Wesley, Reading, Massachusetts 1969.
Murchland, J. D.: A New Method for Finding All Elementary Paths in a Complete Directed Graph, Transport Network Theory Unit, London School of Economics, Report LSE-TNT-22, 1965.
Tarjan, R.: Depth-first Search and Linear Graph Algorithms (Working paper) Computer Science Department, Stanford University 1971.
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Brucker, P. A decomposition algorithm for shortest paths in a network with many strongly connected components. Zeitschrift für Operations Research 18, 177–180 (1974). https://doi.org/10.1007/BF02026598
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DOI: https://doi.org/10.1007/BF02026598