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