Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
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ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
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ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
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Information Sciences: an International Journal
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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
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LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
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CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
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Information Systems
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SAGA'07 Proceedings of the 4th international conference on Stochastic Algorithms: foundations and applications
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Theoretical Computer Science
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FAST'13 Proceedings of the 11th USENIX conference on File and Storage Technologies
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We consider the following problem: Given a subset S of size n of a universe {0,..., u-1}, construct a minimal perfect hash function for S, i.e., a bijection h from S to {0,..., n - 1}. The parameters of interest are the space needed to store h, its evaluation time, and the time required to compute h from S. The number of bits needed for the representation of h, ignoring the other parameters, has been thoroughly studied and is known to be n log e + loglog u ± O(log n), where "log" denotes the binary logarithm. A construction by Schmidt and Siegel uses O(n + loglogu) bits and offers constant evaluation time, but the time to find h is not discussed. We present a simple randomized scheme that uses n log e+log log u+o(n+log log u) bits and has constant evaluation time and O(n + log log u) expected construction time.