Abstract
We give an Õ(2n/3) quantum algorithm for the 0-1 Knapsack problem with n variables and an Õ(2n/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 Õ(2n/4) for its quantum query complexity and an Õ(2n/3) upper bound. We also give a 2(1 − α)n/2 quantum algorithm for satisfiability of CNF formulas with no restrictions on clause size, but with the number of clauses bounded by cn for a constant c, where n is the number of variables. Here α is a constant depending on c.
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Arvind, V., Schuler, R. (2003). The Quantum Query Complexity of 0-1 Knapsack and Associated Claw Problems. In: Ibaraki, T., Katoh, N., Ono, H. (eds) Algorithms and Computation. ISAAC 2003. Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24587-2_19
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DOI: https://doi.org/10.1007/978-3-540-24587-2_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20695-8
Online ISBN: 978-3-540-24587-2
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