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
A reliable randomized algorithm for the closest-pair problem
Journal of Algorithms
Efficient Strongly Universal and Optimally Universal Hashing
MFCS '99 Proceedings of the 24th International Symposium on Mathematical Foundations of Computer Science
Hash and Displace: Efficient Evaluation of Minimal Perfect Hash Functions
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
Universal Hashing and k-Wise Independent Random Variables via Integer Arithmetic without Primes
STACS '96 Proceedings of the 13th Annual Symposium on Theoretical Aspects of Computer Science
Efficient Minimal Perfect Hashing in Nearly Minimal Space
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Simple Minimal Perfect Hashing in Less Space
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Journal of Algorithms
Balanced allocation and dictionaries with tightly packed constant size bins
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
De dictionariis dynamicis pauco spatio utentibus
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
External perfect hashing for very large key sets
Proceedings of the sixteenth ACM conference on Conference on information and knowledge management
Practical perfect hashing in nearly optimal space
Information Systems
Design strategies for minimal perfect hash functions
SAGA'07 Proceedings of the 4th international conference on Stochastic Algorithms: foundations and applications
Simple and space-efficient minimal perfect hash functions
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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In typical applications of hashing algorithms the amount of data to be stored is often too large to fit into internal memory. In this case it is desirable to find the data with as few as possible non-consecutive or at least non-oblivious probes into external memory. Extending a static scheme of Pagh [11] we obtain new randomized algorithms for maintaining hash tables, where a hash function can be evaluated in constant time and by probing only one external memory cell or O(1) consecutive external memory cells. We describe a dynamic version of Pagh's hashing scheme achieving 100% table utilization but requiring (2+ε)nlogn space for the hash function encoding as well as (3+ε)nlogn space for the auxiliary data structure. Update operations are possible in expected constant amortized time. Then we show how to reduce the space for the hash function encoding and the auxiliary data structure to O(nloglogn). We achieve 100% utilization in the static version (and thus a minimal perfect hash function) and 1–ε utilization in the dynamic case.