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Faster Deterministic Sorting and Searching in Linear Space
, 1995
"... We present a significant improvement on linear space deterministic sorting and searching. On a unitcost RAM with word size w, an ordered set of n wbit keys (viewed as binary strings or integers) can be maintained in O ` min ` p log n; log n log w + log log n; log w log log n " time per op ..."
Abstract

Cited by 39 (7 self)
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We present a significant improvement on linear space deterministic sorting and searching. On a unitcost RAM with word size w, an ordered set of n wbit keys (viewed as binary strings or integers) can be maintained in O ` min ` p log n; log n log w + log log n; log w log log n " time per operation, including insert, delete, member search, and neighbour search. The cost for searching is worstcase while the cost for updates is amortized. For range queries, there is an additional cost of reporting the found keys. As an application, n keys can be sorted in linear space at a worstcase cost of O \Gamma n p log n \Delta . The best previous method for deterministic sorting and searching in linear space has been the fusion trees which supports queries in O(logn= log log n) amortized time and sorting in O(n log n= log log n) worstcase time. We also make two minor observations on adapting our data structure to the input distribution and on the complexity of perfect hashing. 1 I...