Simpler and faster dictionaries on the AC0 RAM

Abstract

We consider the static dictionary problem of using 0(n) w-bit words to store n w-bit keys for fast retrieval on a w-bit AC RAM, i.e., on a RAM with a word length of w bits whose instruction set is arbitrary, except that each instruction must be realizable through an unbounded-fanin circuit of constant depth and wo(1) size. We improve the best known upper bound for moderate values of w relative to n. If w/log n = (log log n)o(1), query time (log log log n)o(1) is achieved, and if additionally w/log n ≥ (log log n)1+ε for some fixed ε < 0, the query time is constant. For both of these special cases, the best previous upper bound was O(log log n). A new lower bound is also observed.