On dynamic bit-probe complexity

Abstract

This paper presents several advances in the understanding of dynamic data structures in the bit-probe model: - We improve the lower bound record for dynamic language membership problems to Ω((lgn/lg lg n) 2). Surpassing Ω(lg n) was listed as the first open problem in a survey by Miltersen. - We prove a bound of Ω(lg n/lg lg lg n) for maintaining partial sums in ℤ/2ℤ. Previously, the known bounds were Ω(lg n/lg lg n) and O(lg n). - We prove a surprising and tight upper bound of O(lgn/lg lg n) for predecessor problems. We use this to obtain the same upper bound for dynamic word and prefix problems in group-free monoids. © Springer-Verlag Berlin Heidelberg 2005.