Combinatorica

, Volume 8, Issue 3, pp 235–247 | Cite as

A lower bound for finding predecessors in Yao's cell probe model

  • M. Ajtai
Article

Abstract

LetL be the set consisting of the firstq positive integers. We prove in this paper that there does not exist a data structure for representing an arbitrary subsetA ofL which uses poly (¦A¦) cells of memory (where each cell holdsc logq bits of information) and which the predecessor inA of an arbitraryx≦q can be determined by probing only a constant (independent ofq) number of cells. Actually our proof gives more: the theorem remains valid if this number is less thanε log logq, that is D. E. Willard's algorithm [2] for finding the predecessor inO(log logq) time is optimal up to a constant factor.

AMS subject classification code (1980)

68B15 

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References

  1. [1]
    M.Ajtai, M.Fredman and J.Komlós, Hash Functions for priority Queues,Proceedings of the 24th Annual Symposium on FOCS, 1983.Google Scholar
  2. [2]
    D. E. Willard, Logarithmic worst case range queries are possible in spaceO(n), Inform. Proc. Letter,17 (1983), 81–89.Google Scholar
  3. [3]
    A. Yao, Should tables be sorted,JACM 28, 3 (July 1981), 615–628.Google Scholar

Copyright information

© Akadémiai Kiadó 1988

Authors and Affiliations

  • M. Ajtai
    • 1
  1. 1.IBM Almaden Research CenterUSA

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