Advertisement

Shortest Paths

Part of the Algorithms and Combinatorics 21 book series (AC, volume 21)

Keywords

Short Path Undirected Graph Edge Weight Short Path Problem Short Path Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

General Literature

  1. Ahuja, R.K., Magnanti, T.L., and Orlin, J.B. [1993]: Network Flows. Prentice-Hall, Englewood Cliffs 1993, Chapters 4 and 5Google Scholar
  2. Cormen, T.H., Leiserson, C.E., and Rivest, R.L. [1990]: Introduction to Algorithms. MIT Press, Cambridge 1990, Chapters 23, 25 and 26Google Scholar
  3. Dreyfus, S.E. [1969]: An appraisal of some shortest path algorithms. Operations Research 17 (1969), 395–412MATHGoogle Scholar
  4. Gallo, G., and Pallottino, S. [1988]: Shortest paths algorithms. Annals of Operations Research 13 (1988), 3–79MathSciNetGoogle Scholar
  5. Gondran, M., and Minoux, M. [1984]: Graphs and Algorithms. Wiley, Chichester 1984, Chapter 2MATHGoogle Scholar
  6. Lawler, E.L. [1976]: Combinatorial Optimization: Networks and Matroids. Holt, Rinehart and Winston, New York 1976, Chapter 3MATHGoogle Scholar
  7. Schrijver, A. [2003]: Combinatorial Optimization: Polyhedra and Efficiency. Springer, Berlin 2003, Chapters 6-8MATHGoogle Scholar
  8. Tarjan, R.E. [1983]: Data Structures and Network Algorithms. SIAM, Philadelphia 1983, Chapter 7Google Scholar

Cited References

  1. Ahuja, R.K., Mehlhorn, K., Orlin, J.B., and Tarjan, R.E. [1990]: Faster algorithms for the shortest path problem. Journal of the ACM 37 (1990), 213–223CrossRefMathSciNetMATHGoogle Scholar
  2. Albrecht, C., Korte, B., Schietke, J., and Vygen, J. [2002]: Maximum mean weight cycle in a digraph and minimizing cycle time of a logic chip. Discrete Applied Mathematics 123 (2002), 103–127CrossRefMathSciNetMATHGoogle Scholar
  3. Bellman, R.E. [1958]: On a routing problem. Quarterly of Applied Mathematics 16 (1958), 87–90MathSciNetMATHGoogle Scholar
  4. Cherkassky, B.V., and Goldberg, A.V. [1999]: Negative-cycle detection algorithms. Mathematical Programming A 85 (1999), 277–311CrossRefMathSciNetMATHGoogle Scholar
  5. Dial, R.B. [1969]: Algorithm 360: shortest path forest with topological order. Communications of the ACM 12 (1969), 632–633CrossRefGoogle Scholar
  6. Dijkstra, E.W. [1959]: A note on two problems in connexion with graphs. Numerische Mathematik 1 (1959), 269–271CrossRefMathSciNetMATHGoogle Scholar
  7. Edmonds, J., and Karp, R.M. [1972]: Theoretical improvements in algorithmic efficiency for network flow problems. Journal of the ACM 19 (1972), 248–264CrossRefMATHGoogle Scholar
  8. Fakcharoenphol, J., and Rao, S. [2001]: Planar graphs, negative edge weights, shortest paths, and near-linear time. Proceedings of the 42nd Annual Symposium on Foundations of Computer Science (2001), 232–241Google Scholar
  9. Floyd, R.W. [1962]: Algorithm 97-shortest path. Communications of the ACM 5 (1962), 345Google Scholar
  10. Ford, L.R. [1956]: Network flow theory. Paper P-923, The Rand Corporation, Santa Monica 1956Google Scholar
  11. Fredman, M.L., and Tarjan, R.E. [1987]: Fibonacci heaps and their uses in improved network optimization problems. Journal of the ACM 34 (1987), 596–615CrossRefMathSciNetGoogle Scholar
  12. Fredman, M.L., and Willard, D.E. [1994]: Trans-dichotomous algorithms for minimum spanning trees and shortest paths. Journal of Computer and System Sciences 48 (1994), 533–551CrossRefMathSciNetMATHGoogle Scholar
  13. Goldberg, A.V. [1995]: Scaling algorithms for the shortest paths problem. SIAM Journal on Computing 24 (1995), 494–504CrossRefMathSciNetMATHGoogle Scholar
  14. Henzinger, M.R., Klein, P., Rao, S., and Subramanian, S. [1997]: Faster shortest-path algorithms for planar graphs. Journal of Computer and System Sciences 55 (1997), 3–23CrossRefMathSciNetMATHGoogle Scholar
  15. Johnson, D.B. [1982]: A priority queue in which initialization and queue operations take O(log log D) time. Mathematical Systems Theory 15 (1982), 295–309MATHGoogle Scholar
  16. Karp, R.M. [1978]: A characterization of the minimum cycle mean in a digraph. Discrete Mathematics 23 (1978), 309–311MathSciNetMATHGoogle Scholar
  17. Megiddo, N. [1979]: Combinatorial optimization with rational objective functions. Mathematics of Operations Research 4 (1979), 414–424MathSciNetMATHGoogle Scholar
  18. Megiddo, N. [1983]: Applying parallel computation algorithms in the design of serial algorithms. Journal of the ACM 30 (1983), 852–865CrossRefMathSciNetMATHGoogle Scholar
  19. Moore, E.F. [1959]: The shortest path through a maze. Proceedings of the International Symposium on the Theory of Switching, Part II, Harvard University Press, 1959, 285–292Google Scholar
  20. Orlin, J.B. [1993]: A faster strongly polynomial minimum cost flow algorithm. Operations Research 41 (1993), 338–350MathSciNetMATHCrossRefGoogle Scholar
  21. Pettie, S., and Ramachandran, V. [2002]: Computing shortest paths with comparisons and additions. Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms (2002), 267–276; to appear in SIAM Journal on ComputingGoogle Scholar
  22. Pettie, S. [2004]: A new approach to all-pairs shortest paths on real-weighted graphs. Theoretical Computer Science 312 (2004), 47–74CrossRefMathSciNetMATHGoogle Scholar
  23. Radzik, T. [1993]: Parametric flows, weighted means of cuts, and fractional combinatorial optimization. In: Complexity in Numerical Optimization (P.M. Pardalos, ed.), World Scientific, Singapore 1993Google Scholar
  24. Raman, R. [1997]: Recent results on the single-source shortest paths problem. ACM SIGACT News 28 (1997), 81–87CrossRefGoogle Scholar
  25. Thorup, M. [1999]: Undirected single-source shortest paths with positive integer weights in linear time. Journal of the ACM 46 (1999), 362–394CrossRefMathSciNetMATHGoogle Scholar
  26. Thorup, M. [2000]: On RAM priority queues. SIAM Journal on Computing 30 (2000), 86–109CrossRefMathSciNetMATHGoogle Scholar
  27. Thorup, M. [2003]: Integer priority queues with decrease key in constant time and the single source shortest paths problem. Proceedings of the 35th Annual ACM Symposium on Theory of Computing (2003), 149–158Google Scholar
  28. Warshall, S. [1962]: A theorem on boolean matrices. Journal of the ACM 9 (1962), 11–12CrossRefMathSciNetMATHGoogle Scholar
  29. Zwick, U. [2002]: All pairs shortest paths using bridging sets and rectangular matrix multiplication. Journal of the ACM 49 (2002), 289–317CrossRefMathSciNetGoogle Scholar
  30. Zwick, U. [2004]: A slightly improved sub-cubic algorithm for the all pairs shortest paths problem with real edge lengths. Algorithms and Computation-ISAAC 2004; LNCS 3341 (R. Fleischer, G. Trippen, eds.), Springer, Berlin 2004, pp. 921–932Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Personalised recommendations