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External Memory Algorithms for Outerplanar Graphs

  • Anil Maheshwari
  • Norbert Zeh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1741)

Abstract

We present external memory algorithms for outerplanarity testing, embedding outerplanar graphs, breadth-first search (BFS) and depth-first search (DFS) in outerplanar graphs, and finding a \( \frac{2} {3} \) -separator of size 2 for a given outerplanar graph. Our algorithms take O(sort(N)) I/Os and can easily be improved to take O(perm(N)) I/Os, as all these problems have linear time solutions in internal memory. For BFS, DFS, and outerplanar embedding we show matching lower bounds.

Keywords

Planar Graph Outer Face Internal Memory Outerplanar Graph Dual Tree 
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.
    Y.-J. Chiang, M. T. Goodrich, E. F. Grove, R. Tamassia, D. E. Vengroff, J. S. Vitter. External-memory graph algorithms. Proc. 6th SODA, Jan. 1995.Google Scholar
  2. 2.
    T. H. Cormen, C. E. Leiserson, R. L. Rivest. Introduction to Algorithms. MIT Press, 1990.Google Scholar
  3. 3.
    G. N. Frederickson. Searching among intervals in compact routing tables. Algorithmica, 15:448–466, 1996.zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    F. Harary. Graph Theory. Addison-Wesley, 1969.Google Scholar
  5. 5.
    D. Hutchinson, A. Maheshwari, N. Zeh. An external memory data structure for shortest path queries. Proc. COCOON’99, LNCS 1627, pp. 51–50, July 1999.Google Scholar
  6. 6.
    J. van Leeuwen. Handbook of Theoretical Computer Science, Vol. A: Algorithms and Complexity. MIT Press, 1990.Google Scholar
  7. 7.
    R. J. Lipton, R. E. Tarjan. A separator theorem for planar graphs. SIAM J. on Applied Mathematics, 36(2):177–189, 1979.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    S. L. Mitchell. Linear algorithms to recognize outerplanar and maximal outerplanar graphs. Inf. Proc. Letters, 9(5):229–232, Dec. 1979.zbMATHCrossRefGoogle Scholar
  9. 9.
    K. Munagala, A. Ranade. I/O-complexity of graph algorithms. Proc. 10th SODA, Jan. 1999.Google Scholar
  10. 10.
    J. S. Vitter. External memory algorithms. Proc. 17th ACM Symp. on Principles of Database Systems, June 1998.Google Scholar
  11. 11.
    J. S. Vitter and E. A. M. Shriver. Algorithms for parallel memory I: Two-level memories. Algorithmica, 12(2-3):110–147, 1994.zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    N. Zeh. An External-Memory Data Structure for Shortest Path Queries. Diplomarbeit, Fak. f. Math. und Inf. Friedrich-Schiller-Univ. Jena, Nov. 1998.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Anil Maheshwari
    • 1
  • Norbert Zeh
    • 1
  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada

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