A lower bound for the dictionary problem under a hashing model

Abstract

A fundamental open question in data structures concerns the existence of a dictionary data structure that processes the operations in constant amortized time and uses space polynomial in the dictionary size. The complexity of the dictionary problem is studied under a multilevel hashing model that is based on A.C. Yao's (1981) cell probe model, and it is proved that dictionary operations require log-algorithmic amortized time jn this model. The model encompasses many known solutions to the dictionary problem, and the result is the first nontrivial lower bound for the problem in a reasonably general model that takes into account the limited wordsize of memory locations and realistically measures the cost of update operations. This lower bound separates the deterministic and randomized complexities of the problem under this model.<>