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Automata, Languages and Programming pp 372–381Cite as

Efficient Techniques for Maintaining Multidimensional Keys in Linked Data Structures (Extended Abstract)

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1644))

Abstract

We describe a general paradigm for maintaining multidimensional keys in linked data structures designed for one-dimensional keys. We improve existing bounds and achieve new results in a simple way, without giving up the structural and topological properties of the underlying data structures. This is particularly important, as it allows us to exploit many properties of one-dimensional searching, and makes our approach amenable to practical implementations.

Partially supported by EU ESPRIT Long Term Research Project ALCOM-IT under contract no. 20244.

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References

  1. G.M. Adel’son-Vel’skii and E M. Landis. An algorithm for the organization of information. Soviet Mathematics Doklady, 3 (1962), 1259–1263.

    Google Scholar 

  2. Samuel W. Bent, Daniel D. Sleator and Robert E. Tarjan. Biased search trees. SIAM Journal on Computing 14 (1985), 545–568.

    Article  MathSciNet  Google Scholar 

  3. Jon L. Bentley and Robert Sedgewick. Fast algorithms for sorting and searching strings. In Proc. 8th ACM-SIAM Symp. on Discrete Algorithms (1997), 360–369.

    Google Scholar 

  4. Gerth Stølting Brodal. Finger search trees with constant insertion time. In Proc. 9th ACM-SIAM Symp. on Discrete Algorithms (1998), 540–549.

    Google Scholar 

  5. Mark R. Brown and Robert E. Tarjan. Design and analysis of a data structure for representing sorted lists. SIAM Journal on Computing 9 (1980), 594–614.

    Article  MathSciNet  Google Scholar 

  6. Henry A. Clampett. Randomized binary searching with the tree structures. Communications of ACM 7 (1964), 163–165.

    Article  Google Scholar 

  7. Paul F. Dietz and Daniel D. Sleator. Two algorithms for maintaining order in a list. In Proc. 19th ACM Symp. on Theory of Computing (1987), 365–372.

    Google Scholar 

  8. James R. Driscoll, Neil Sarnak, Daniel D. Sleator, and Robert E. Tarjan. Making data structures persistent. J. of Computer and System Sciences 38 (1989), 86–124.

    Article  MathSciNet  Google Scholar 

  9. Paolo Ferragina and Roberto Grossi. The String B-Tree: A new data structure for string search in external memory and its applications. Journal of ACM, to appear. Preliminary version in Proc. 27th ACM Symp. on Theory of Comp. (1995) 693–702.

    Google Scholar 

  10. Teofilo F. Gonzalez. The on-line d-dimensional dictionary problem. In Proc. 3rd ACM-SIAM Symp. on Discrete Algorithms (1992), 376–385.

    Google Scholar 

  11. Ralf H. Gueting and Hans-Peter Kriegel. Multidimensional B-tree: An efficient dynamic file structure for exact match queries. In Proc. 10th GI Conference, Informatik-Fachberichte, Springer, 33 (1980), 375–388.

    MathSciNet  Google Scholar 

  12. Scott Huddleston and Kurt Mehlhorn. A new data structure for representing sorted lists. Acta Informatica 17 (1982), 157–184.

    Article  MathSciNet  Google Scholar 

  13. Robert W. Irving. Sufix binary search trees. Research Report, Department of Computer Science, University of Glasgow, April 1997.

    Google Scholar 

  14. Christos Levcopoulos and Mark H. Overmars. A balanced search tree with O(1) worst-case update time. Acta Informatica 26 (1988), 269–277.

    Article  MathSciNet  Google Scholar 

  15. Udi Manber and Eugene W. Myers. Sufix arrays: A new method for on-line string searches. SIAM Journal on Computing 22 (1993), 935–948.

    Article  MathSciNet  Google Scholar 

  16. Kurt Mehlhorn. Dynamic binary search. SIAM J. on Computing 8 (1979), 175–198.

    Article  MathSciNet  Google Scholar 

  17. Kurt Mehlhorn. Data structures and algorithms: 1. Searching and sorting, Springer, (1984).

    Google Scholar 

  18. Jürg Nievergelt and Edward M. Reingold. Binary search trees of bounded balance. SIAM Journal on Computing 2 (1973), 33–43.

    Article  MathSciNet  Google Scholar 

  19. Raimund Seidel and Cecilia R. Aragon. Randomized search trees. Algorithmica 16 (1996), 464–497.

    Article  MathSciNet  Google Scholar 

  20. Daniel D. Sleator and Robert E. Tarjan. Self-adjusting binary search trees. Journal of ACM 32 (1985), 652–686.

    Article  MathSciNet  Google Scholar 

  21. Robert E. Tarjan. Data structures and network algorithms, CBMS-NSF Reg. Conf. Ser. Appl. Math. 44, SIAM (1983).

    Google Scholar 

  22. Vijay K. Vaishnavi. Multidimensional height-balanced trees. IEEE Transactions on Computers C-33 (1984), 334–343.

    Article  MathSciNet  Google Scholar 

  23. Vijay K. Vaishnavi. Multidimensional balanced binary trees. IEEE Transactions on Computers C-38 (1989), 968–985.

    Article  MathSciNet  Google Scholar 

  24. Vijay K. Vaishnavi. On k-dimensional balanced binary trees. Journal of Computer and System Sciences 52 (1996), 328–348.

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Università di Pisa, Italy

    Roberto Grossi

  2. Dipartimento di Informatica, Sistemi e Produzione, Università di Roma “Tor Vergata”, Italy

    Giuseppe F. Italiano

Authors
  1. Roberto Grossi
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  2. Giuseppe F. Italiano
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Editor information

Editors and Affiliations

  1. Institute for Computer Science, Academy of Sciences of the Czech Republic, Pod vodarenskou vezi 2, 182 07, Prague 8 - Liben, Czech Republic

    Jirí Wiedermann

  2. ILLC-WINS-University of Amsterdam, Plantage Muidergracht 24, 1018, TV, Amsterdam, The Netherlands

    Peter van Emde Boas

  3. BRICS, Department of Computer Science, University of Aarhus, Ny Munkegade, Bldg. 540, DK, 8000, Aarhus C, Denmark

    Mogens Nielsen

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© 1999 Springer-Verlag Berlin Heidelberg

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Grossi, R., Italiano, G.F. (1999). Efficient Techniques for Maintaining Multidimensional Keys in Linked Data Structures (Extended Abstract). In: Wiedermann, J., van Emde Boas, P., Nielsen, M. (eds) Automata, Languages and Programming. Lecture Notes in Computer Science, vol 1644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48523-6_34

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  • DOI: https://doi.org/10.1007/3-540-48523-6_34

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66224-2

  • Online ISBN: 978-3-540-48523-0

  • eBook Packages: Springer Book Archive

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