Lower bounds for predecessor searching in the cell probe model

We consider a fundamental problem in data structures, static predecessor searching: Given a subset S of size n from the universe [m], store S so that queries of the form “What is the predecessor of x in S?” can be answered efficiently. We study this problem in the cell probe model introduced by Yao [A.C.-C. Yao, Should tables be sorted, J. Assoc. Comput. Mach. 28 (3) (1981) 615–628]. Recently, Beame and Fich [P. Beame, F. Fich, Optimal bounds for the predecessor problem and related problems, J. Comput. System Sci. 65 (1) (2002) 38–72] obtained optimal bounds as functions of either m or n only on the number of probes needed by any deterministic query scheme if the associated storage scheme uses only nO(1) cells of word size (logm)O(1) bits. We give a new lower bound proof for this problem that matches the bounds of Beame and Fich. Our lower bound proof has the following advantages: it works for randomised query schemes too, while Beame and Fich’s proof works for deterministi...

• Type: Conference
• Year: 2003
• Where: COCO
• Authors: Pranab Sen
• Keywords: COCO 2003, Deterministic Query Schemes, Lower Bound, Query Schemes