Algorithmica

, Volume 72, Issue 2, pp 369–378

Worst-Case Optimal Tree Layout in External Memory

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Abstract

Consider laying out a fixed-topology binary tree of N nodes into external memory with block size B so as to minimize the worst-case number of block memory transfers required to traverse a path from the root to a node of depth D. We prove that the optimal number of memory transfers is
$$\begin{aligned} \begin{cases} \varTheta( {D \over\lg(1{+}B)} ) & \mathrm{when}~D = O(\lg N), \\ \varTheta( {\lg N \over\lg(1{+}{B \lg N \over D} )} ) & \mathrm{when}~D = \varOmega(\lg N)~\mathrm{and}~D = O(B \lg N), \\ \varTheta( {D \over B} ) & \mathrm{when}~D = \varOmega(B \lg N). \end{cases} \end{aligned}$$

Keywords

Data structures Trees External-memory 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Erik D. Demaine
    • 1
  • John Iacono
    • 2
    • 3
  • Stefan Langerman
    • 4
  1. 1.MIT Computer Science and Artificial Intelligence LaboratoryCambridgeUSA
  2. 2.Polytechnic Institute of New York University (Formerly Polytechnic University)BrooklynUSA
  3. 3.MADALGO—Center for Massive Data Algorithmics, a Center of the Danish National Research FoundationAarhus UniversityAarhus NDenmark
  4. 4.Département d’informatique, Université Libre de BruxellesF.R.S.-FNRSBrusselsBelgium

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