A time-space tradeoff for element distinctness
In "A Time Space Tradeoff for Sorting on non-Oblivious Machines", Borodin et al. [B - 81] proved that to sort n elements requires TS = Ω(n2) where T=time and S=space on a comparison based branching problem. Although element distinctness and sorting are equivalent problems on a computation tree, the stated tradeoff result does not immediately follow for element distinctness or indeed for any decision problem. In this paper, we are able to show that TS=Ω(n3/2) for deciding element distinctness (or the sign of a permutation).
KeywordsDirected Acyclic Graph Computation Tree Main Lemma Adjacent Pair Arithmetic Circuit
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