Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
Dynamic Perfect Hashing: Upper and Lower Bounds
SIAM Journal on Computing
Membership in Constant Time and Almost-Minimum Space
SIAM Journal on Computing
Optimal static range reporting in one dimension
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Succinct indexable dictionaries with applications to encoding k-ary trees and multisets
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Low Redundancy in Static Dictionaries with Constant Query Time
SIAM Journal on Computing
A New Universal Class of Hash Functions and Dynamic Hashing in Real Time
ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming
Efficient Minimal Perfect Hashing in Nearly Minimal Space
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
On Universal Classes of Extremely Random Constant-Time Hash Functions
SIAM Journal on Computing
The Bloomier filter: an efficient data structure for static support lookup tables
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
On dynamic range reporting in one dimension
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Succinct dynamic dictionaries and trees
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Derandomized constructions of k-wise (almost) independent permutations
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
De-amortized Cuckoo Hashing: Provable Worst-Case Performance and Experimental Results
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Maintaining external memory efficient hash tables
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Design strategies for minimal perfect hash functions
SAGA'07 Proceedings of the 4th international conference on Stochastic Algorithms: foundations and applications
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We develop dynamic dictionaries on the word RAM that use asymptotically optimal space, up to constant factors, subject to insertions and deletions, and subject to supporting perfect-hashing queries and/or membership queries, each operation in constant time with high probability. When supporting only membership queries, we attain the optimal space bound of $\theta(n lg \frac{u}{n})$ bits, where n and u are the sizes of the dictionary and the universe, respectively. Previous dictionaries either did not achieve this space bound or had time bounds that were only expected and amortized. When supporting perfect-hashing queries, the optimal space bound depends on the range {1, 2, ..., n+t} of hashcodes allowed as output. We prove that the optimal space bound is $\theta(n lg lg \frac{u}{n} + n lg \frac{n}{t+1})$ bits when supporting only perfect-hashing queries, and it is $\theta(n lg \frac{u}{n} + n lg \frac{n}{t+1})$ bits when also supporting membership queries. All upper bounds are new, as is the $\Omega({\it n}lg\frac{n}{t+1})$ lower bound.