Graph Problems: Polynomial-Time

Abstract

Algorithmic graph problems constitute approximately one third of the problems in this catalog. Problems from other sections could have been formulated equally well in terms of graphs, such as bandwidth minimization and finite-state automata optimization. Identifying the name of a graph-theoretic invariant or problem is one of the primary skills of a good algorist. Indeed, the catalog will tell you exactly how to proceed as soon as you figure out your particular problem’s name.

In this section, we deal only with problems for which there are efficient algorithms to solve them. As there is often more than one way to model a given application, it makes sense to look here before proceeding on to the harder formulations.

Keywords

Short Path Span Tree Planar Graph Minimum Span Tree Linear Extension 
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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Bibliography

  1. [AMO93]
    R. Ahuja, T. Magnanti, and J. Orlin. Network Flows. Prentice Hall, Englewood Cliffs NJ, 1993.MATHGoogle Scholar
  2. [Ata98]
    M. Atallah. Algorithms and Theory of Computation Handbook. CRC, 1998.Google Scholar
  3. [Eve79a]
    S. Even. Graph Algorithms. Computer Science Press, Rockville MD, 1979.MATHGoogle Scholar
  4. [Gib85]
    A. Gibbons. Algorithmic Graph Theory. Cambridge Univ. Press, 1985.Google Scholar
  5. [MN99]
    K. Mehlhorn and S. Naher. LEDA: A platform for combinatorial and geometric computing. Cambridge University Press, 1999.Google Scholar
  6. [SLL02]
    J. Siek, L. Lee, and A. Lumsdaine. The Boost Graph Library: user guide and reference manual. Addison Wesley, Boston, 2002.Google Scholar
  7. [TNX08]
    K. Thulasiraman, T. Nishizeki, and G. Xue. The Handbook of Graph Algorithms and Applications, volume 1: Theory and Optimization. Chapman-Hall/CRC, 2008.Google Scholar
  8. [vL90a]
    J. van Leeuwen. Graph algorithms. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science: Algorithms and Complexity, volume A, pages 525–631. MIT Press, 1990.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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