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Faster Deterministic Dictionaries
 In 11 th Annual ACM Symposium on Discrete Algorithms (SODA
, 1999
"... We consider static dictionaries over the universe U = on a unitcost RAM with word size w. Construction of a static dictionary with linear space consumption and constant lookup time can be done in linear expected time by a randomized algorithm. In contrast, the best previous deterministic a ..."
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Cited by 9 (5 self)
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We consider static dictionaries over the universe U = on a unitcost RAM with word size w. Construction of a static dictionary with linear space consumption and constant lookup time can be done in linear expected time by a randomized algorithm. In contrast, the best previous deterministic algorithm for constructing such a dictionary with n elements runs in time O(n ) for # > 0. This paper narrows the gap between deterministic and randomized algorithms exponentially, from the factor of to an O(log n) factor. The algorithm is weakly nonuniform, i.e. requires certain precomputed constants dependent on w. A byproduct of the result is a lookup time vs insertion time tradeo# for dynamic dictionaries, which is optimal for a certain class of deterministic hashing schemes.
A TradeOff For WorstCase Efficient Dictionaries
"... We consider dynamic dictionaries over the universe U = {0, 1}^w on a unitcost RAM with word size w and a standard instruction set, and present a linear space deterministic dictionary accommodating membership queries in time (log log n)^O(1) and updates in time (log n)^O(1), where n is the size of t ..."
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Cited by 7 (2 self)
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We consider dynamic dictionaries over the universe U = {0, 1}^w on a unitcost RAM with word size w and a standard instruction set, and present a linear space deterministic dictionary accommodating membership queries in time (log log n)^O(1) and updates in time (log n)^O(1), where n is the size of the set stored. Previous solutions either had query time (log n) 18 or update time 2 !( p log n) in the worst case.
A New Tradeoff for Deterministic Dictionaries
, 2000
"... . We consider dictionaries over the universe U = f0; 1g w on a unitcost RAM with word size w and a standard instruction set. We present a linear space deterministic dictionary with membership queries in time (log log n) O(1) and updates in time (log n) O(1) , where n is the size of the se ..."
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Cited by 1 (0 self)
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. We consider dictionaries over the universe U = f0; 1g w on a unitcost RAM with word size w and a standard instruction set. We present a linear space deterministic dictionary with membership queries in time (log log n) O(1) and updates in time (log n) O(1) , where n is the size of the set stored. This is the rst such data structure to simultaneously achieve query time (log n) o(1) and update time O(2 (log n) c ) for a constant c < 1. 1 Introduction Among the most fundamental data structures is the dictionary. A dictionary stores a subset S of a universe U , oering membership queries of the form \x 2 S?". The result of a membership query is either 'no' or a piece of satellite data associated with x. Updates of the set are supported via insertion and deletion of single elements. Several performance measures are of interest for dictionaries: The amount of space used, the time needed to answer queries, and the time needed to perform updates. The most ecient dictionar...