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Hard Knapsack Problems

Author

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  • Vasek Chvátal

    (McGill University, Montreal, Canada)

Abstract

We consider a class of algorithms which use the combined powers of branch-and-bound, dynamic programming and rudimentary divisibility arguments for solving the zero-one knapsack problem. Our main result identifies a class of instances of the problem which are difficult to solve by such algorithms. More precisely, if reading the data takes t units of time, then the time required to solve the problem grows exponentially with the square root of t .

Suggested Citation

  • Vasek Chvátal, 1980. "Hard Knapsack Problems," Operations Research, INFORMS, vol. 28(6), pages 1402-1411, December.
    • Handle: RePEc:inm:oropre:v:28:y:1980:i:6:p:1402-1411
    DOI: 10.1287/opre.28.6.1402
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    Cited by:

    1. Liu, Yipeng & Koehler, Gary J., 2010. "Using modifications to Grover's Search algorithm for quantum global optimization," European Journal of Operational Research, Elsevier, vol. 207(2), pages 620-632, December.
    2. Zonghao Gu & George L. Nemhauser & Martin W. P. Savelsbergh, 1999. "Lifted Cover Inequalities for 0-1 Integer Programs: Complexity," INFORMS Journal on Computing, INFORMS, vol. 11(1), pages 117-123, February.
    3. Chia‐Shin Chung & Ming S. Hung & Walter O. Rom, 1988. "A hard knapsack problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(1), pages 85-98, February.

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