Journal of Combinatorial Optimization

, Volume 17, Issue 4, pp 347–366 | Cite as

A successive approximation algorithm for the multiple knapsack problem

  • Zhenbo Wang
  • Wenxun Xing


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.


Multiple knapsack problem Approximation algorithm Worst-case analysis 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijingChina

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