Weighted Graph Algorithms

  • Steven S. Skiena


The data structures and traversal algorithms of Chapter 5 provide the basic building blocks for any computation on graphs. However, all the algorithms presented there dealt with unweighted graphs—i.e., graphs where each edge has identical value or weight.

There is an alternate universe of problems for weighted graphs. The edges of road networks are naturally bound to numerical values such as construction cost, traversal time, length, or speed limit. Identifying the shortest path in such graphs proves more complicated than breadth-first search in unweighted graphs, but opens the door to a wide range of applications.


Short Path Span Tree Minimum Span Tree Edge Weight Weighted Graph 
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.


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  1. [AMO93]
    R. Ahuja, T. Magnanti, and J. Orlin. Network Flows. Prentice Hall, Englewood Cliffs NJ, 1993.zbMATHGoogle Scholar
  2. [CC97]
    W. Cook and W. Cunningham. Combinatorial Optimization. Wiley, 1997.Google Scholar
  3. [EK72]
    J. Edmonds and R. Karp. Theoretical improvements in the algorithmic efficiency for network flow problems. J. ACM, 19:248–264, 1972.CrossRefzbMATHGoogle Scholar
  4. [FF62]
    L. Ford and D. R. Fulkerson. Flows in Networks. Princeton University Press, Princeton NJ, 1962.zbMATHGoogle Scholar
  5. [PS03]
    S. Pemmaraju and S. Skiena. Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Cambridge University Press, New York, 2003.zbMATHGoogle Scholar
  6. [RS96]
    H. Rau and S. Skiena. Dialing for documents: an experiment in information theory. Journal of Visual Languages and Computing, pages 79–95, 1996.Google Scholar
  7. [Wes00]
    D. West. Introduction to Graph Theory. Prentice-Hall, Englewood Cliffs NJ, second edition, 2000.Google Scholar

Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  1. 1.Department of Computer ScienceState University of New York at Stony BrookNew YorkUSA

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