Two Simplified Algorithms for Maintaining Order in a List

  • Michael A. Bender
  • Richard Cole
  • Erik D. Demaine
  • Martin Farach-Colton
  • Jack Zito
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2461)


In the Order-Maintenance Problem, the objective is to maintain a total order subject to insertions, deletions, and precedence queries. Known optimal solutions, due to Dietz and Sleator, are complicated. We present new algorithms that match the bounds of Dietz and Sleator. Our solutions are simple, and we present experimental evidence that suggests that they are superior in practice.


Total Order Weight Cost List Element Virtual Tree Order Maintenance 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A. Andersson and O. Petersson. Approximate indexed lists. Journal of Algorithms, 29(2):256–276, 1998.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    L. Arge and J. Vitter. Optimal dynamic interval management in external memory. In FOCS, 1996.Google Scholar
  3. [3]
    P. Dietz and D. Sleator. Two algorithms for maintaining order in a list. In STOC, 1987.Google Scholar
  4. [4]
    P. F. Dietz. Maintaining order in a linked list. In STOC, 1982.Google Scholar
  5. [5]
    P. F. Dietz, J. I. Seiferas, and J. Zhang. A tight lower bound for on-line monotonic list labeling. In SWAT, 1994.Google Scholar
  6. [6]
    P. F. Dietz and J. Zhang. Lower bounds for monotonic list labeling. In SWAT, 1990.Google Scholar
  7. [7]
    A. Itai, A. Konheim, and M. Rodeh. A sparse table implementation of priority queues. In ICALP, 1981.Google Scholar
  8. [8]
    J. Nievergelt and E.M. Reingold. Binary search trees of bounded balance. SIComp, 2:33–43, 1973.zbMATHMathSciNetGoogle Scholar
  9. [9]
    W. Pugh. Skip lists: a probabilistic alternative to balanced trees. In WADS, 1989.Google Scholar
  10. [10]
    A.K. Tsakalidis. Maintaining order in a generalized linked list. Acta Informatica, 21(1):101–112, May 1984.zbMATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    D. Willard. Inserting and deleting records in blocked sequential files. Technical Report TM81-45193-5, Bell Laboratories, 1981.Google Scholar
  12. [12]
    D. Willard. Maintaining dense sequential files in a dynamic environment. In STOC, 1982.Google Scholar
  13. [13]
    D. Willard. Good worst-case algorithms for inserting and deleting records in dense sequential files. In SIGMOD, 1986.Google Scholar
  14. [14]
    D. Willard. A density control algorithm for doing insertions and deletions in a sequentially ordered file in good worst-case time. Information and Computation, 97(2):150–204, 1992.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Michael A. Bender
    • 1
  • Richard Cole
    • 2
  • Erik D. Demaine
    • 3
  • Martin Farach-Colton
    • 4
    • 5
  • Jack Zito
    • 1
  1. 1.Dept of Computer ScienceSUNY Stony BrookNYUSA
  2. 2.Courant InstituteNew York UniversityNew YorkUSA
  3. 3.MIT Laboratory for Computer ScienceCambridgeUSA
  4. 4.Google Inc.Mountain ViewUSA
  5. 5.Department of Computer ScienceRutgers UniversityPiscatawayUSA

Personalised recommendations