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Dynamic Perfect Hashing: Upper and Lower Bounds
, 1990
"... The dynamic dictionary problem is considered: provide an algorithm for storing a dynamic set, allowing the operations insert, delete, and lookup. A dynamic perfect hashing strategy is given: a randomized algorithm for the dynamic dictionary problem that takes O(1) worstcase time for lookups and ..."
Abstract

Cited by 127 (13 self)
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The dynamic dictionary problem is considered: provide an algorithm for storing a dynamic set, allowing the operations insert, delete, and lookup. A dynamic perfect hashing strategy is given: a randomized algorithm for the dynamic dictionary problem that takes O(1) worstcase time for lookups and O(1) amortized expected time for insertions and deletions; it uses space proportional to the size of the set stored. Furthermore, lower bounds for the time complexity of a class of deterministic algorithms for the dictionary problem are proved. This class encompasses realistic hashingbased schemes that use linear space. Such algorithms have amortized worstcase time complexity \Omega(log n) for a sequence of n insertions and
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 ..."
Abstract

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.