On (Dynamic) Range Minimum Queries in External Memory

  • Lars Arge
  • Johannes Fischer
  • Peter Sanders
  • Nodari Sitchinava
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8037)


We study the one-dimensional range minimum query (RMQ) problem in the external memory model. We provide the first space-optimal solution to the batched static version of the problem. On an instance with N elements and Q queries, our solution takes Θ(sort(N + Q)) = Θ(\(N+Q \over B\) log M /B \(N+Q \over B\)) I/O complexity and O(N + Q) space, where M is the size of the main memory and B is the block size. This is a factor of O(log M /B N) improvement in space complexity over the previous solutions. We also show that an instance of the batched dynamic RMQ problem with N updates and Q queries can be solved in O (\(N+Q \over B\) \(\log^{2}_{M /B}\) \(N+Q \over B\)) I/O complexity and O(N + Q) space.


Internal Node Internal Memory Query Answer Range Minimum Dynamic Array 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Lars Arge
    • 1
  • Johannes Fischer
    • 2
  • Peter Sanders
    • 2
  • Nodari Sitchinava
    • 2
  1. 1.MADALGOAarhus UniversityAarhusDenmark
  2. 2.Karlsruhe Institute of TechnologyKarlsruheGermany

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