A successive approximation algorithm for the multiple knapsack problem

Zhenbo Wang () and Wenxun Xing
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Zhenbo Wang: Tsinghua University
Wenxun Xing: Tsinghua University

Journal of Combinatorial Optimization, 2009, vol. 17, issue 4, No 1, 347-366

Abstract: Abstract It is well-known that the multiple knapsack problem is NP-hard, and does not admit an FPTAS even for the case of two identical knapsacks. Whereas the 0-1 knapsack problem with only one knapsack has been intensively studied, and some effective exact or approximation algorithms exist. A natural approach for the multiple knapsack problem is to pack the knapsacks successively by using an effective algorithm for the 0-1 knapsack problem. This paper considers such an approximation algorithm that packs the knapsacks in the nondecreasing order of their capacities. We analyze this algorithm for 2 and 3 knapsack problems by the worst-case analysis method and give all their error bounds.

Keywords: Multiple knapsack problem; Approximation algorithm; Worst-case analysis (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-007-9116-y

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