Abstract
Addressing a problem of Fredman and Willard, we implement fusion trees in deterministic linear space using AC 0 instructions only. More precisely, we show that a subset of {0,…,2 w - 1} of size n can be maintained using linear space under insertion, deletion, predecessor, and successor queries, with O( log n log log n ) amortized time per operation on a RAM with word size w, where the only computational instructions allowed on the RAM are functions in AC 0 . The AC 0 instructions used are not all available on today's computers.
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