The Quantum Query Complexity of 0-1 Knapsack and Associated Claw Problems

@inproceedings{Arvind2003TheQQ,
  title={The Quantum Query Complexity of 0-1 Knapsack and Associated Claw Problems},
  author={V. Arvind and R. Schuler},
  booktitle={ISAAC},
  year={2003}
}
We give an O(2 n/3) quantum algorithm for the 0-1 Knapsack problem with n variables and an O(2 n/3 n d ) quantum algorithm for 0-1 Integer Linear Programs with n variables and d inequalities. To investigate lower bounds we formulate a symmetric claw problem corresponding to 0-1 Knapsack. For this problem we establish a lower bound of O(2 n/4) for its quantum query complexity and an O(2 n/3) upper bound. We also give a 2(1 − α)n/2 quantum algorithm for satisfiability of CNF formulas with no… Expand
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