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

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.