This paper addresses the more general problem in which a fixed collection of bin sizes is allowed. Three efficient approximation algorithms are described and ...

Abstract. For bin packing, the input consists of n items with sizes s1,...,sn ∈ [0, 1] which have to be assigned to a minimum number of bins of size 1.

We provide the first improvement in over three decades and show that one can find a solution of cost $OPT + O(\log OPT \cdot \log \log OPT)$ in polynomial time.

This is achieved by rounding a fractional solution to the Gilmore--Gomory LP relaxation using the partial coloring method from discrepancy theory. The result is ...

A well-studied special case of bin packing is the 3-partition problem, where n items of size > 1/4 have to be packed in a minimum number of bins of capacity ...

The necessary difference is called the discrepancy. We establish a surprising connection between bin packing and Beck's problem: The additive integrality gap of ...

Jun 7, 2011 · As Peter pointed out, the 3-partition problem is NP-hard even when the sizes are between 1/3−δ and 1/3+δ for any constant δ>0.

May 8, 2015 · In section 4, we give a brief sketch of the algorithm that gives a better approximation guarantee for the bin-packing with rejection problem.

Missing: Discrepancy Theory.

The chapter surveys the literature on worst- case and average-case behavior of approximation algorithms for one-dimensional bin packing, using each type of ...