Skip to main content
SpringerLink
Log in
Book cover

Scandinavian Workshop on Algorithm Theory

SWAT 2000: Algorithm Theory - SWAT 2000 pp 433–447Cite as

On External-Memory MST, SSSP, and Multi-way Planar Graph Separation

Extended Abstract

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1851))

Abstract

Recently external memory graph algorithms have received considerable attention because massive graphs arise naturally in many applications involving massive data sets. Even though a large number of I/O-efficient graph algorithms have been developed, a number of fundamental problems still remain open. In this paper we develop an improved algorithm for the problem of computing a minimum spanning tree of a general graph, as well as new algorithms for the single source shortest paths and the multi-way graph separation problems on planar graphs.

Supported in part by the National Science Foundation through ESS grant EIA-9870734, RI grant EIA-9972879 and CAREER grant EIA-9984099. E-mail: large@cs.duke.edu.

BRICS (Basic Research in Computer Science, Center of Danish National Research Foundation). Supported in part by the IST Programme of the EU under contract number IST-1999-14186 (ALCOM-FT). E-mail: gerth@brics.dk.

Supported in part by the National Science Foundation through ESS grant EIA-9870734 and RI grant EIA-9972879. E-mail: laura@cs.duke.edu.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Abello, A. L. Buchsbaum, and J. R. Westbrook. A functional approach to external graph algorithms. In Proc. Annual European Symposium on Algorithms, LNCS 1461, pages 332–343, 1998.

    Google Scholar 

  2. P. K. Agarwal, L. Arge, T. M. Murali, K. Varadarajan, and J. S. Vitter. I/O-efficient algorithms for contour line extraction and planar graph blocking. In Proc. ACM-SIAM Symp. on Discrete Algorithms, pages 117–126, 1998.

    Google Scholar 

  3. A. Aggarwal and J. S. Vitter. The Input/Output complexity of sorting and related problems. Communications of the ACM, 31(9):1116–1127, 1988.

    Article  MathSciNet  Google Scholar 

  4. ARC/INFO. Understanding GIS—the ARC/INFO method. ARC/INFO, 1993. Rev. 6 for workstations.

    Google Scholar 

  5. L. Arge. The buffer tree: A new technique for optimal I/O-algorithms. In Proc. Workshop on Algorithms and Data Structures, LNCS 955, pages 334–345, 1995. A complete version appears as BRICS technical report RS-96-28, University of Aarhus.

    Google Scholar 

  6. L. Arge. The I/O-complexity of ordered binary-decision diagram manipulation. In Proc. Int. Symp. on Algorithms and Computation, LNCS 1004, pages 82–91, 1995. A complete version appears as BRICS technical report RS-96-29, University of Aarhus.

    Chapter  Google Scholar 

  7. L. Arge, L. Toma, and J. S. Vitter. I/O-efficient algorithms for problems on grid-based terrains. In Proc. Workshop on Algorithm Engineering and Experiments, 2000.

    Google Scholar 

  8. O. Borůvka. O jistém problému minimálním. Práca Moravské Přírodovědecké Společnosti, 3:37–58, 1926.

    Google Scholar 

  9. G. S. Brodal and J. Katajainen. Worst-case efficient external-memory priority queues. In Proc. Scandinavian Workshop on Algorithms Theory, LNCS 1432, pages 107–118, 1998.

    Google Scholar 

  10. A. L. Buchsbaum, M. Goldwasser, S. Venkatasubramanian, and J. R. Westbrook. On external memory graph traversal. In Proc. ACM-SIAM Symp. on Discrete Algorithms, pages 859–860, 2000.

    Google Scholar 

  11. A. L. Buchsbaum and J. R. Westbrook. Maintaining hierarchical graph views. In Proc. ACM-SIAM Symp. on Discrete Algorithms, pages 566–575, 2000.

    Google Scholar 

  12. Y.-J. Chiang, M. T. Goodrich, E. F. Grove, R. Tamassia, D. E. Vengroff, and J. S. Vitter. External-memory graph algorithms. In Proc. ACM-SIAM Symp. on Discrete Algorithms, pages 139–149, 1995.

    Google Scholar 

  13. F. Chin, J. Lam, and I. Chen. Efficient parallel algorithms for some graph problems. Communications of ACM, 1982.

    Google Scholar 

  14. R. Cole and U. Vishkin. Approximate parallel scheduling. II. Applications to logarithmic-time optimal parallel graph algorithms. Information and Computation, 92(1):1–47, May 1991.

    Google Scholar 

  15. T. H. Cormen, C. E. Leiserson, and R. L. Rivest. Introduction to Algorithms. The MIT Press, Cambridge, Mass., 1990.

    MATH  Google Scholar 

  16. E. Feuerstein and A. Marchetti-Spaccamela. Memory paging for connectivity and path problems in graphs. LNCS, 762:416–425, 1993.

    Google Scholar 

  17. G. N. Frederickson. Fast algorithms for shortest paths in planar graphs, with applications. SIAM Journal of Computing, 16:1004–1022, 1987.

    Article  MATH  Google Scholar 

  18. M. Goodrich. Planar separators and parallel polygon triangulation. Journal of Computer and System Sciences, 51(3):374–389, 1995.

    Article  MathSciNet  Google Scholar 

  19. D. Hutchinson, A. Maheshwari, and N. Zeh. An external memory data structure for shortest path queries. In Proc. 5th Annual Int. Conf. Computing and Combinatorics, number 1627 in LNCS. Springer-Verlag, July 1999.

    Chapter  Google Scholar 

  20. D. E. Knuth. Sorting and Searching, volume 3 of The Art of Computer Programming. Addison-Wesley, Reading MA, second edition, 1998.

    Google Scholar 

  21. D. Kozen. The Design and Analysis of Algorithms. Springer, Berlin, 1992.

    Google Scholar 

  22. V. Kumar and E. Schwabe. Improved algorithms and data structures for solving graph problems in external memory. In Proc. IEEE Symp. on Parallel and Distributed Processing, pages 169–177, 1996.

    Google Scholar 

  23. R. J. Lipton and R. E. Tarjan. A separator theorem for planar graphs. SIAM Journal of Applied Math., 36:177–189, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  24. A. Maheshwari and N. Zeh. External memory algorithms for outerplanar graphs. Manuscript, 1999.

    Google Scholar 

  25. K. Munagala and A. Ranade. I/O-complexity of graph algorithm. In Proc. ACM-SIAM Symp. on Discrete Algorithms, pages 687–694, 1999.

    Google Scholar 

  26. M. H. Nodine, M. T. Goodrich, and J. S. Vitter. Blocking for external graph searching. Algorithmica, 16(2):181–214, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  27. J. H. Reif, editor. Synthesis of Parallel Algorithms, chapter 3, pages 115–194. Morgan Kaufmann, 1993.

    Google Scholar 

  28. R. E. Tarjan. Data structures and network algorithms. SIAM, Philadelphia, 1983.

    Google Scholar 

  29. J. D. Ullman and M. Yannakakis. The input/output complexity of transitive closure. Annals of Mathematics and Artificial Intellegence, 3:331–360, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  30. J. S. Vitter. External memory algorithms (invited tutorial). In Proc. of the 1998 ACM Symposium on Principles of Database Systems, pages 119–128, 1998.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Duke University, Durham, NC 27708-0129, USA

    Lars Arge & Laura Toma

  2. University of Aarhus, DK-8000, Århus C, Denmark

    Gerth Stølting Brodal

Authors
  1. Lars Arge
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gerth Stølting Brodal
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Laura Toma
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Arge, L., Brodal, G.S., Toma, L. (2000). On External-Memory MST, SSSP, and Multi-way Planar Graph Separation. In: Algorithm Theory - SWAT 2000. SWAT 2000. Lecture Notes in Computer Science, vol 1851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44985-X_37

Download citation

  • DOI: https://doi.org/10.1007/3-540-44985-X_37

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67690-4

  • Online ISBN: 978-3-540-44985-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation