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Bin Packing with Fixed Number of Bins Revisited

  • Klaus Jansen
  • Stefan Kratsch
  • Dániel Marx
  • Ildikó Schlotter
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6139)

Abstract

As Bin Packing is NP-hard already for k = 2 bins, it is unlikely to be solvable in polynomial time even if the number of bins is a fixed constant. However, if the sizes of the items are polynomially bounded integers, then the problem can be solved in time n O(k) for an input of length n by dynamic programming. We show, by proving the W[1]-hardness of Unary Bin Packing (where the sizes are given in unary encoding), that this running time cannot be improved to f(kn O(1) for any function f(k) (under standard complexity assumptions). On the other hand, we provide an algorithm for Bin Packing that obtains in time \(2^{O(k\log^2 k)}+O(n)\) a solution with additive error at most 1, i.e., either finds a packing into k + 1 bins or decides that k bins do not suffice.

Keywords

Large Item Small Item Medium Item Item Size Feasible Mapping 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Klaus Jansen
    • 1
  • Stefan Kratsch
    • 2
  • Dániel Marx
    • 3
  • Ildikó Schlotter
    • 4
  1. 1.Institut für InformatikChristian-Albrechts-Universität KielKielGermany
  2. 2.Max-Planck-Institut für InformatikSaarbrückenGermany
  3. 3.Tel Aviv UniversityIsrael
  4. 4.Budapest University of Technology and EconomicsBudapestHungary

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