Error correcting codes, perfect hashing circuits, and deterministic dynamic dictionaries

Abstract

The dictionaries of size n over the finite universe U = {0, 1}w were considered, and a new technique, called error correcting codes, was introduced for their implementation. This approach was used to construct, for any ε >0, a deterministic solution to the dynamic dictionary problem using linear space, with worst case time O(nε) for insertions and deletions, and worst case time O(1) for lookups. This is the first deterministic solution to the dynamic dictionary problem with linear space, constant query time, and non-trivial update time. In particular, a solution was obtained to the static dictionary problem with O(n) space, worst case query time O(1), and deterministic initialization time (n1+ε).