Abstract
We present a significant improvement on linear space deterministic sorting and searching. On a unit-cost RAM with word size w, an ordered set of n w-bit keys (viewed as binary strings or integers) can be maintained in O(min{[/spl radic/(logn)][logn/logw+loglogn][logwloglogn]}) time per operation, including insert, delete, member search, and neighbour search. The cost for searching is worst-case while the cost for updates is amortized. As an application, n keys can be sorted in linear at O(n/spl radic/(logn)) worst-case cost. The best previous method for deterministic sorting and searching in linear space has been the fusion trees which supports updates and queries in O(logn/loglogn) amortized time and sorting in O(nlogn/loglogn) worst-case time. We also make two minor observations on adapting our data structure to the input distribution and on the complexity of perfect hashing.