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Predecessor Queries in Constant Time?

  • Marek Karpinski
  • Yakov Nekrich
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3669)

Abstract

In this paper we design a new static data structure for batched predecessor queries. In particular, our data structure supports \(O(\sqrt{{\rm log}n})\) queries in O(1) time per query and requires \(O(n^{\epsilon\sqrt{{\rm log}n}})\) space for any ε > 0. This is the first o(N) space and O(1) amortized time data structure for arbitrary \(N = \Omega(n^{\epsilon\sqrt{{\rm log}n}})\) where N is the size of the universe. We also present a data structure that answers O(log log N) predecessor queries in O(1) time per query and requires \(O(n^{\epsilon{\rm log log} {\it N}})\) space for any ε > 0. The method of solution relies on a certain way of searching for predecessors of all elements of the query in parallel.

In a general case, our approach leads to a data structure that supports p(n) queries in \(O(\sqrt{{\rm log} n}/p(n))\) time per query and requires O(n \(^{p({\it n})}\)) space for any \(p(n) =O(\sqrt{{\rm log}n})\), and a data structure that supports p(N) queries in O(log log N/p(N)) time per query and requires O(n \(^{p({\it N})}\)) space for any p(N)=O(log log N).

Keywords

Data Structure Hash Function Priority Queue Query Time Word Size 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Marek Karpinski
    • 1
  • Yakov Nekrich
    • 1
  1. 1.Dept. of Computer ScienceUniversity of Bonn 

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