# Shortest paths algorithms: Theory and experimental evaluation

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## Abstract

We conduct an extensive computational study of shortest paths algorithms, including some very recent algorithms. We also suggest new algorithms motivated by the experimental results and prove interesting theoretical results suggested by the experimental data. Our computational study is based on several natural problem classes which identify strengths and weaknesses of various algorithms. These problem classes and algorithm implementations form an environment for testing the performance of shortest paths algorithms. The interaction between the experimental evaluation of algorithm behavior and the theoretical analysis of algorithm performance plays an important role in our research.

## Keywords

Graph algorithms Network optimization Shortest paths Theory and experimental evaluation of algorithms## Preview

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## References

- [1]R.K. Ahuja, K. Mehlhorn, J.B. Orlin and R.E. Tarjan, “Faster algorithms for the shortest path problem”,
*J. Assoc. Comput. Mach.*37 (2) (1990) 213–223.zbMATHMathSciNetGoogle Scholar - [2]R.E. Bellman, “On a routing problem”,
*Quart. Appl. Math.*16 (1958) 87–90.MathSciNetzbMATHGoogle Scholar - [3]P. van Emde Boas, R. Kaas and E. Zijlstra, “Design and implementation of an efficient priority queue”,
*Math. Syst. Theory*10 (1977) 99–127.zbMATHCrossRefGoogle Scholar - [4]T.H. Cormen, C.E. Leiserson and R.L. Rivest,
*Introduction to Algorithms*(MIT Press, Cambridge, MA, 1990).zbMATHGoogle Scholar - [5]E.V. Denardo and B.L. Fox, “Shortest-route methods: 1. Reaching, pruning, and buckets”,
*Operations Research*27 (1979) 161–186.zbMATHMathSciNetGoogle Scholar - [6]R.B. Dial, “Algorithm 360: Shortest path forest with topological ordering”,
*Comm. ACM*12 (1969) 632–633.CrossRefGoogle Scholar - [7]R.B. Dial, F. Glover, D. Karney and D. Klingman, “A computational analysis of alternative algorithms and labeling techniques for finding shortest path trees”,
*Networks*9 (1979) 215–248.zbMATHMathSciNetGoogle Scholar - [8]E.W. Dijkstra, “A note on two problems in connection with graphs”,
*Numer. Math.*1 (1959) 269–271.zbMATHCrossRefMathSciNetGoogle Scholar - [9]R.E. Erickson, C.L. Monma and A.F. Veinott Jr., “Send-and-split method for minimum-concave-cost network flows”,
*Math. of Oper. Res.*12 (1979) 634–664.MathSciNetGoogle Scholar - [10]L.R. Ford Jr., and D.R. Fulkerson,
*Flows in Networks*(Princeton Univ. Press, Princeton, NJ, 1962)zbMATHGoogle Scholar - [11]M.L. Fredman and R.E. Tarjan, “Fibonacci heaps and their uses in improved network optimization algorithms”,
*J. Assoc. Comput. Mach.*34 (1987) 596–615.MathSciNetGoogle Scholar - [12]M.L. Fredman and D.E. Willard, “Trans-dichotomous algorithms for minimum spanning trees and shortest paths”,
*J. Comp. and Syst. Sci.*48 (1994) 533–551.zbMATHCrossRefMathSciNetGoogle Scholar - [13]H.N. Gabow and R.E. Tarjan, “Faster scaling algorithms for network problems”,
*SIAM J. Comput.*(1989) 1013–1036.Google Scholar - [14]G. Gallo and S. Pallottino, “Shortest paths algorithms”,
*Annals of Oper. Res.*13 (1988) 3–79.MathSciNetGoogle Scholar - [15]F. Glover, R. Glover and D. Klingman, “Computational study of an improved shortest path algorithm”,
*Networks*14 (1984) 25–37.Google Scholar - [16]F. Glover, D. Klingman and N. Phillips, “A new polynomially bounded shortest paths algorithm”,
*Oper. Res.*33 (1985) 65–73.zbMATHMathSciNetCrossRefGoogle Scholar - [17]A.V. Goldberg, “Scaling algorithms for the shortest paths problem”, in:
*Proceedings 4th ACM-SIAM Symposium on Discrete Algorithms*(1993) 222–231.Google Scholar - [18]A.V. Goldberg and T. Radzik, “A heuristic improvement of the Bellman-Ford algorithm”,
*Applied Math. Let.*6 (1993) 3–6.zbMATHCrossRefMathSciNetGoogle Scholar - [19]M.S. Hung and J.J. Divoky, “A computational study of efficient shortest path algorithms”,
*Comput. Oper. Res.*15 (1988) 567–576.zbMATHCrossRefMathSciNetGoogle Scholar - [20]D.S. Johnson and C.C. McGeoch, eds.,
*Network Flows and Matching: First DIMACS Implementation Challenge*(AMS, 1993).Google Scholar - [21]A. Kershenbaum, “A note on finding shortest paths trees”,
*Networks*11 (1981) 399.MathSciNetGoogle Scholar - [22]E.L. Lawler,
*Combinatorial Optimization: Networks and Matroids*(Holt Reinhart, and Winston, New York 1976).zbMATHGoogle Scholar - [23]B.Ju. Levit and B.N. Livshits,
*Neleneinye Setevye Transportnye Zadachi*(Transport, Moscow, 1972), in Russian.Google Scholar - [24]J-F. Mondou, T.G. Crainic and S. Nguyen, “Shortest path algorithms: A computational study with the C programming language”,
*Comput. Oper. Res.*18 (1991) 767–786.zbMATHCrossRefGoogle Scholar - [25]E.F. Moore, “The shortest path through a maze”, in:
*Proceedings of the Int. Symp. on the Theory of Switching*(Harvard University Press, 1959) 285–292.Google Scholar - [26]S. Pallottino, “Shortest-path methods: Complexity, interrelations and new propositions”,
*Networks*14 (1984) 257–267.zbMATHGoogle Scholar - [27]U. Pape, “Implementation and efficiency of Moore algorithms for the shortest root problem”,
*Math. Prog.*7 (1974) 212–222.zbMATHCrossRefMathSciNetGoogle Scholar - [28]D. Shier and C. Witzgall, “Properties of labeling methods for determining shortest paths trees”,
*J. Res. Natl. Bur. Stand.*86 (1981) 317–330.zbMATHMathSciNetGoogle Scholar - [29]R.E. Tarjan,
*Data Structures and Network Algorithms*(Society for Industrial and Applied Mathematics, Philadelphia, PA, 1983).Google Scholar