The Hardness of Speeding-up Knapsack

  • Sandeep Sen


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  Omega(sqrt(n)) rounds even by using 2^sqrt(n) 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.
Keywords lower-bounds, parallel algorithms, algebraic decision tree
How to Cite
Sen, S. (1998). The Hardness of Speeding-up Knapsack. BRICS Report Series, 5(14).