Shortest-path algorithms: Taxonomy and annotation

We have evolved a classification scheme to characterize algorithms for solving shortestpath problems. The algorithms are classified according to (A) the problem type, i.e., the question being asked about the given network; (B) the input type, i.e., the salient features of the given network which impact on the design of the algorithm and selection of data structures; and (C) the type of underlying technique employed to solve the problem. An annotated bibliography of 79 selected references on shortest-path algorithms is included. We have also provided a more complete listing of 222 references carefully culled out of a larger body of literature on shortest-path algorithms through the year 1979.

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[81]  T. A. J. Nicholson,et al.  Finding the Shortest Route between Two Points in a Network , 1966, Comput. J..

[82]  Donald B. Johnson,et al.  Efficient Algorithms for Shortest Paths in Sparse Networks , 1977, J. ACM.

[83]  Jin Y. Yen,et al.  Finding the Lengths of All Shortest paths in N -Node Nonnegative-Distance Complete Networks Using 12N3 Additions and N3 Comparisons , 1972, JACM.

[84]  O. G. Alekseev,et al.  An algorithm for determining the shortest path on a network graph , 1971 .

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[89]  Darwin Klingman,et al.  A Note on Finding All Shortest Paths , 1974 .

[90]  B. Carré.  An Algebra for Network Routing Problems , 1971 .

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[93]  J. A. Hillier,et al.  A Method for Finding the Shortest Route Through a Road Network , 1960 .

[94]  Alan J. Hoffman,et al.  Finding all shortest distances in a directed network , 1972 .

[95]  Harry M. Markowitz,et al.  A note on shortest path, assignment, and transportation problems , 1963 .

[96]  Ronald F. Kirby,et al.  The minimum route problem for networks with turn penalties and prohibitions , 1969 .

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[114]  Alan M. Frieze.  Shortest path algorithms for knapsack type problems , 1976, Math. Program..

[115]  Michael L. Fredman,et al.  New Bounds on the Complexity of the Shortest Path Problem , 1976, SIAM J. Comput..

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[117]  Ellis L. Johnson.  On shortest paths and sorting , 1972, ACM Annual Conference.

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[124]  T. C. Hu,et al.  Shortcut in the decomposition algorithm for shortest paths in a network , 1969 .

[125]  Bently A. Crane.  Path Finding with Associative Memory , 1968, IEEE Transactions on Computers.

[126]  Santosh Kumar,et al.  The Routing Problem with "K" Specified Nodes , 1966, Oper. Res..

[127]  Robert A. Wagner,et al.  A Shortest Path Algorithm for Edge-Sparse Graphs , 1976, J. ACM.

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[137]  Marc Rosseel,et al.  Letter to the Editor - Comments on a Paper By Romesh Saigal: "A Constrained Shortest Route Problem" , 1968, Oper. Res..

[138]  Gideon Yuval,et al.  An Algorithm for Finding All Shortest Paths Using N^(2.81) Infinite-Precision Multiplications , 1976, Inf. Process. Lett..

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[140]  Frank O. Hadlock,et al.  A shortest path algorithm for grid graphs , 1977, Networks.

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[142]  V. V. Rodionov.  The parametric problem of shortest distances , 1968 .

[143]  Aarni Perko.  Some Computational Notes on the Shortest Route Problem , 1965, Comput. J..

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[147]  Edward Minieka,et al.  On computing sets of shortest paths in a graph , 1974, Commun. ACM.

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