2013 IEEE 54th Annual Symposium on Foundations of Computer Science (1991)

San Juan, Puerto Rico

Oct. 1, 1991 to Oct. 4, 1991

ISBN: 0-8186-2445-0

pp: 612-621

R. Sundar , Dept. of Comput. Sci., New York Univ., NY, USA

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.

INDEX TERMS

randomized complexities, polynomial space, update costs, deterministic complexities, dictionary problem, data structures, constant amortized time, multilevel hashing model, cell probe model, log-algorithmic amortized time, nontrivial lower bound, limited wordsize, memory locations

CITATION

R. Sundar,
"A lower bound for the dictionary problem under a hashing model",

*2013 IEEE 54th Annual Symposium on Foundations of Computer Science*, vol. 00, no. , pp. 612-621, 1991, doi:10.1109/SFCS.1991.185427