Bin Packing with Fixed Number of Bins Revisited

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 nO(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(k)

• Type: Journal
• Year: 2010
• Where: SWAT
• Authors: Klaus Jansen, Stefan Kratsch, Dániel Marx, Ildikó Schlotter
• Keywords: Algorithms, Bin Packing, Standard Complexity Assumptions, SWAT 2010, Unary Bin Packing