Abstract
We analyze the expected difference between the solutions to the integer and linear versions of the 0–1 Knapsack Problem. This difference is of interest partly because it may help understand the efficiency of a well-known fast backtracking algorithm for the integer 0–1 Knapsack Problem. We show that, under a fairly reasonable input distribution, the expected difference is 0(log2n/n); for a somewhat more restricted subclass of input distribution, we also show that the expected difference is Ω(l/n).
This work was facilitated by the use of MACSYMA, a large symbolic Manipulation program developed at the MIT Laboratory for Computer Science and supported by the National Aeronautics and Space Administration under grant NSG 1323, by the Office of Naval Research under grant N00014-77-C-0641, by the U.S. Department of Energy under grant ET-78-C-02-4687, and by the U.S. Air Force under grant F49620-79-C-020.
Supported by the National Science Foundation under grant MCS79-04997.
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© 1982 Birkhäuser Boston, Inc.
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Lueker, G.S. (1982). On the Average Difference between the Solutions to Linear and Integer Knapsack Problems. In: Disney, R.L., Ott, T.J. (eds) Applied Probability-Computer Science: The Interface Volume 1. Progress in Computer Science, vol 2. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-5791-2_22
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DOI: https://doi.org/10.1007/978-1-4612-5791-2_22
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