A lower bound for the dictionary problem under a hashing model

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.<<ETX>>

[1]  Larry Carter,et al.  Universal Classes of Hash Functions , 1979, J. Comput. Syst. Sci..

[2]  Prof. Dr. Kurt Mehlhorn,et al.  Data Structures and Algorithms 1 , 1984, EATCS.

[3]  Robert E. Tarjan,et al.  Self-adjusting binary search trees , 1985, JACM.

[4]  Dan E. Willard.  New Trie Data Structures Which Support Very Fast Search Operations , 1984, J. Comput. Syst. Sci..

[5]  Kurt Mehlhorn,et al.  On the Complexity of a Game Related to the Dictionary Problem , 1990, SIAM J. Comput..

[6]  Robert E. Tarjan,et al.  Data structures and network algorithms , 1983, CBMS-NSF regional conference series in applied mathematics.

[7]  Andrew Chi-Chih Yao,et al.  Should Tables Be Sorted? , 1981, JACM.

[8]  János Komlós,et al.  Hash functions for priority queues , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[9]  János Komlós,et al.  Storing a sparse table with O(1) worst case access time , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[10]  Alfred V. Aho,et al.  Storing a dynamic sparse table , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[11]  Miklós Ajtai,et al.  A lower bound for finding predecessors in Yao's cell probe model , 1988, Comb..

[12]  Friedhelm Meyer auf der Heide,et al.  Dynamic perfect hashing: upper and lower bounds , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[13]  W. Hoeffding.  Probability Inequalities for sums of Bounded Random Variables , 1963 .

[14]  Michael L. Fredman,et al.  BLASTING through the information theoretic barrier with FUSION TREES , 1990, STOC '90.