Space-time tradeoffs for oblivious integer multiplication
An extension of a result by Grigoryev is used to derive a lower bound on the space-time product required for integer multiplication when realized by straight-line algorithms. If S is the number of temporary storage locations used by a straight-line algorithm on a random-access machine and T is the number of computation steps, then we show that (S+1)T ⩾ Ω(n2) for binary integer multiplication when the basis for the straight-line algorithm is a set of Boolean functions.
KeywordsBoolean Function Integer Multiplication Combinatorial Argument Pebble Game Oblivious Algorithm
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