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


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.

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  1. [1]

    M.Ajtai, M.Fredman and J.Komlós, Hash Functions for priority Queues,Proceedings of the 24th Annual Symposium on FOCS, 1983.

  2. [2]

    D. E. Willard, Logarithmic worst case range queries are possible in spaceO(n), Inform. Proc. Letter,17 (1983), 81–89.

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    A. Yao, Should tables be sorted,JACM 28, 3 (July 1981), 615–628.

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Ajtai, M. A lower bound for finding predecessors in Yao's cell probe model. Combinatorica 8, 235–247 (1988). https://doi.org/10.1007/BF02126797

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AMS subject classification code (1980)

  • 68B15