The Hardness of Speeding-up Knapsack

Sandeep Sen

August 1998


We show that it is not possible to speed-up the Knapsack problem efficiently in the parallel algebraic decision tree model. More specifically, we prove that any parallel algorithm in the fixed degree algebraic decision tree model that solves the decision version of the Knapsack problem requires tex2html_wrap_inline24 rounds even by using tex2html_wrap_inline26 processors. We extend the result to the PRAM model without bit-operations. These results are consistent with Mulmuley's recent result on the separation of the strongly-polynomial class and the corresponding NC class in the arithmetic PRAM model

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