On Dynamic Bit-Probe Complexity

  • Corina E. Pǎtraşcu
  • Mihai Pǎtraşcu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3580)


This paper presents several advances in the understanding of dynamic data structures in the bit-probe model:

  • We improve the lower bound record for dynamic language membership problems to \(\Omega((\frac{{\rm lg}\ n}{\rm lg \ lg \ {\it n}})^{2})\). Surpassing \(\Omega({\rm lg} \ {\it n})\) was listed as the first open problem in a survey by Miltersen.

  • We prove a bound of \(\Omega(\frac{{\rm lg}\ n}{\rm lg \ lg \ lg \ {\it n}})\) for maintaining partial sums in \({\mathbb Z}/2{\mathbb Z}\). Previously, the known bounds were \(\Omega(\frac{{\rm lg}\ n}{\rm lg \ lg \ {\it n}})\) and \(O({\rm lg}\ n)\).

  • We prove a surprising and tight upper bound of \(O(\frac{{\rm lg} \ {\it n}}{\rm lg \ lg \ {\it n}})\) for predecessor problems. We use this to obtain the same upper bound for dynamic word and prefix problems in group-free monoids.


Word Problem Lower Common Ancestor Dynamic Data Structure Random Query Dynamic Connectivity 
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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  1. 1.
    Thorup, M.: Near-optimal fully-dynamic graph connectivity. In: Proc. 32nd ACM Symposium on Theory of Computing (STOC), pp. 343–350 (2000)Google Scholar
  2. 2.
    Miltersen, P.B., Subramanian, S., Vitter, J.S., Tamassia, R.: Complexity models for incremental computation. Theor. Comp. Sci. 130, 203–236 (1994); Also STACS 1993.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Miltersen, P.B.: Cell probe complexity - a survey. In: Advances in Data Structures Workshop, FSTTCS (1999)Google Scholar
  4. 4.
    Pǎtraşcu, M., Demaine, E.D.: Logarithmic lower bounds in the cell-probe model. In: arXiv:cs.DS/0502041. Based on publications from SODA 2004 and STOC 2004 (2004)Google Scholar
  5. 5.
    Fredman, M.L.: The complexity of maintaining an array and computing its partial sums. Journal of the ACM 29, 250–260 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Fredman, M.L., Saks, M.E.: The cell probe complexity of dynamic data structures. In: Proc. 21st ACM Symposium on Theory of Computing (STOC), pp. 345–354 (1989)Google Scholar
  7. 7.
    Mortensen, C.W., Pagh, R., Pǎtraşcu, M.: On dynamic range reporting in one dimension. In: Proc. 37th ACM Symposium on Theory of Computing, STOC (2004) (to appear)Google Scholar
  8. 8.
    Frandsen, G.S., Miltersen, P.B., Skyum, S.: Dynamic word problems. Journal of the ACM 44, 257–271 (1997); See also FOCS 1993. zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Alstrup, S., Husfeldt, T., Rauhe, T.: Marked ancestor problems. In: Proc. 39th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 534–543 (1998)Google Scholar
  10. 10.
    Krohn, K., Rhodes, J.: Algebraic theory of machines I. Prime decomposition theorem for finite semigroups and machines. Trans. AMS 116, 450–464 (1965)zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Corina E. Pǎtraşcu
    • 1
  • Mihai Pǎtraşcu
    • 2
  1. 1.Harvard University 
  2. 2.MIT 

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