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Disjoint Set Forest Digraph Representation for an Efficient Dominator Tree Construction

  • Wojciech Fraczak
  • Andrew Miller
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7643)

Abstract

We consider a non-orthodox representation of directed graphs which uses the “disjoint set forest” data structure. We show how such a representation can be used in order to efficiently find the dominator tree. Even though the performance of our algorithm does not improve over the already known algorithms for constructing the dominator tree, the approach is new and it gives place to a highly structured and simple to follow proof of correctness.

Keywords

Span Tree Dominator Tree Graph Transformation Input Graph Outgoing Edge 
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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References

  1. 1.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms. The MIT Press and McGraw-Hill Book Company (1989)Google Scholar
  2. 2.
    Georgiadis, L., Tarjan, R.E.: Finding dominators revisited: extended abstract. In: Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2004, pp. 869–878. SIAM (2004)Google Scholar
  3. 3.
    Lowry, E.S., Medlock, C.W.: Object code optimization. Commun. ACM 12, 13–22 (1969), http://doi.acm.org/10.1145/362835.362838 CrossRefGoogle Scholar
  4. 4.
    Prosser, R.T.: Applications of boolean matrices to the analysis of flow diagrams. Papers Presented at the Eastern Joint IRE-AIEE-ACM Computer Conference, IRE-AIEE-ACM 1959 (Eastern), December 1-3, pp. 133–138. ACM Press, New York (1959), http://doi.acm.org/10.1145/1460299.1460314 CrossRefGoogle Scholar
  5. 5.
    Tarjan, R.: Efficiency of a good but not linear set union algorithm. Journal of the Association for Computing Machinery 22(2), 215–225 (1975)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Tarjan, R., Leeuwen, J.: Worst-case analysis of set union algorithms. Journal of the Association for Computing Machinery 31(2), 245–281 (1984)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Wojciech Fraczak
    • 1
    • 2
  • Andrew Miller
    • 2
  1. 1.Université du Québec en OutaouaisGatineauCanada
  2. 2.Benbria CorporationOttawaCanada

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