
Summary: It is shown that a static dictionary that offers constant-time access to \(n\) elements with \(w\)-bit keys and occupies \(O(n)\) words of memory can be constructed deterministically in \(O(n\log n)\) time on a unit-cost RAM with word length \(w\) and a standard instruction set including multiplication. Whereas a randomized construction working in linear expected time was known, the running time of the best previous deterministic algorithm was \(\Omega(n^2)\). Using a standard dynamization technique, the first deterministic dynamic dictionary with constant lookup time and sublinear update time is derived. The new algorithms are weakly nonuniform; i.e., they require access to a fixed number of precomputed constants dependent on \(w\). The main technical tools employed are unit-cost error-correcting codes, word parallelism, and derandomization using conditional expectations.
Data structures, Information storage and retrieval of data, error-correcting codes, deterministic dictionaries
Data structures, Information storage and retrieval of data, error-correcting codes, deterministic dictionaries
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