On Dynamic Bit-Probe Complexity

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

Abstract

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.

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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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