All shortest distances in a graph. An improvement to Dantzig’s inductive algorithm. (English) Zbl 0257.05128


05-04 Software, source code, etc. for problems pertaining to combinatorics
05C35 Extremal problems in graph theory
03E05 Other combinatorial set theory


Algorithm 97
Full Text: DOI


[1] Dantzig, G.B., All shortest routes in a graph, (), 91-92, Dunod, Paris
[2] Dantzig, G.B., All shortest routes from a fixed origin in a graph, (), 85-90, Dunod, Paris · Zbl 0189.24103
[3] Dijkstra, E.W., A note on two problems in connection with graphs, Numerische math., 1, 269-271, (1959) · Zbl 0092.16002
[4] Dreyfus, S.E., An appraisal of some shortest-path algorithms, Operations research, 17, 3, 395-412, (1969) · Zbl 0172.44202
[5] Floyd, R.W., Algorithm 97, shortest path, Commun. A.C.M., 5, 6, 345, (1962)
[6] Roy, B., Algèbre moderne et théorie des graphes, (1970), Dunod Paris, Ch. VII, alg. VII. 12.
[7] Yen, J.Y., A matrix algorithm for solving all shortest routes from a fixed origin in nonnegative networks, TIMS 15th intern. meeting, (1968), Cleveland, Ohio
[8] Yen, J.Y., \(14\)N3 step algorithm for (i) finding all shortest distances from a fixed origin or (ii) detecting negative loops in N-node general networks, 36th ORSA meeting, (1969), Miami Beach, Florida
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