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Lower bounds for monotonic list labeling

  • Paul F. Dietz
  • Ju Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 447)

Abstract

We present optimal lower bound for special cases of the list labeling problem. This problem has diverse practical applications, including implementation of persistent data structures, in the incremental evaluation of computational circuits and in the maintenance of dense sequential files. We prove, under a reasonable restriction on the algorithms, that Ω(n log2n) relabelings are necessary when inserting n items into list monotonically labeled from a label space of size O(n). We also prove that Ω(n log n) relabelings are required in the case of a label space of polynomial size.

Keywords

Boundary Element Smoothness Condition Incremental Evaluation Label Problem Label Space 
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]
    Bowen Alpern, Roger Hoover, Barry K. Rosen, Peter F. Sweeney, and F. Kenneth Zadeck. Incremental evaluation of computational circuits. In Proc. 1st Annual ACM-SIAM Symp. on Disc. Alg., pages 32–42, January 1990.Google Scholar
  2. [2]
    Cecelia R. Aragon and Raimund G. Seidel. Randomized search trees. In Proc. 30th Ann. IEEE Symp. on Foundations of Computer Science, pages 540–545, October 1989.Google Scholar
  3. [3]
    Paul F. Dietz. Maintaining order in a linked list. In Proc. 14th ACM STOC, pages 122–127, May 1982.Google Scholar
  4. [4]
    Paul F. Dietz. Fully persistent arrays. In Workshop on Algorithms and Data Structures, pages 67–74, August 1989.Google Scholar
  5. [5]
    Paul F. Dietz and Daniel D. Sleator. Two algorithms for maintaining order in a list. In Proc. 19th ACM STOC, pages 365–372, May 1987. A revised version of the paper is available that tightens up the analysis.Google Scholar
  6. [6]
    James R. Driscoll, Neil Sarnak, Daniel D. Sleator, and Robert E. Tarjan. Making data structures persistent. JCSS, 38(1):86–124, April 1989.Google Scholar
  7. [7]
    M. Hofri, A. G. Konheim, and A. G. Rodeh. Padded lists revisited. SIAM J. On Computing, 16(6):1073–1114, December 1987.CrossRefGoogle Scholar
  8. [8]
    A. Itai, A. G. Konheim, and M. Rodeh. A spare table implementation of sorted sets. Research Report RC 9146, IBM, November 1981.Google Scholar
  9. [9]
    Robert Melville and David Gries. Sorting and searching using controlled density arrays. Tech Report 78-362, Dept. of Computer Science, Cornell U., 1978.Google Scholar
  10. [10]
    Daniel D. Sleator and Robert E. Tarjan. Amortized efficiency of list update and paging rules. Communications of the ACM, 28(2):202–206, February 1985.CrossRefGoogle Scholar
  11. [11]
    Robert E. Tarjan. Amortized computational complexity. SIAM J. on Alg. and Disc. Meth., 6(2):306–318, 1985.Google Scholar
  12. [12]
    A. K. Tsakalidis. Maintaining order in a generalized linked list. Acta. Info., 21(1):101–112, 1984.Google Scholar
  13. [13]
    Dan E. Willard. Maintaining dense sequential files in a dynamic environment. In Proc. 14th ACM STOC, pages 114–121, May 1982.Google Scholar
  14. [14]
    Dan E. Willard. Good worst-case algorithms for inserting and deleting records in dense sequential files. In ACM SIGMOD 86, pages 251–260, May 1986.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Paul F. Dietz
    • 1
  • Ju Zhang
    • 1
  1. 1.Department of Computer ScienceUniversity of RochesterRochester

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