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

  title={The Quantum Query Complexity of 0-1 Knapsack and Associated Claw Problems},
  author={V. Arvind and R. Schuler},
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
The exponential complexity of satisfiability problems
An algorithm for the satisfiability problem of formulas in conjunctive normal form
  • R. Schuler
  • Computer Science, Mathematics
  • J. Algorithms
  • 2005
On the possibility of faster SAT algorithms
On Moderately Exponential Time for SAT
A Moderately Exponential Time Algorithm for k-IBDD Satisfiability


Quantum lower bound for the collision problem
Quantum lower bounds by quantum arguments
Satisfiability Coding Lemma
  • R. Paturi, P. Pudlák, F. Zane
  • Mathematics, Computer Science
  • Proceedings 38th Annual Symposium on Foundations of Computer Science
  • 1997
Quantum algorithms for element distinctness
  • H. Buhrman, C. Dürr, +4 authors R. D. Wolf
  • Mathematics, Computer Science
  • Proceedings 16th Annual IEEE Conference on Computational Complexity
  • 2001
A fast quantum mechanical algorithm for database search
Quantum lower bounds for the collision and the element distinctness problems
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
  • P. Shor
  • Computer Science, Mathematics
  • SIAM Rev.
  • 1999
Strengths and Weaknesses of Quantum Computing
An Introduction to Quantum Complexity Theory
Quantum Amplitude Amplification and Estimation