A fast asymptotic approximation scheme for bin packing with rejection

A Fast Asymptotic Approximation Scheme for Bin Packing with Rejection

“Bin packing with rejection” is the following problem: Given a list of items with associated sizes and rejection costs, find a packing into unit bins of a subset of the list such that the number of bins used plus the sum of rejection costs of unpacked items is minimized. We show that bin packing with rejection can be reduced to n multiple knapsack problems and, based on techniques for the multi...

An Approximation Scheme for Bin Packing with Conflicts

A sublinear-time approximation scheme for bin packing

From August 17 to August 22, 2008, the Dagstuhl Seminar 08341 Sublinear Algorithms was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and i...

An Asymptotic Competitive Scheme for Online Bin Packing

We study the online bin packing problem, in which a list of items with integral size between 1 to B arrives one at a time. Each item must be assigned in a bin of capacity B upon its arrival without any information on the next items, and the goal is to minimize the number of used bins. We present an asymptotic competitive scheme, i.e., for any > 0, the asymptotic competitive ratio is at most ρ∗ ...

An asymptotic approximation scheme for the concave cost bin packing problem

We consider a generalized one-dimensional bin packing model in which the cost of a bin is a nondecreasing concave function of the utilization of the bin. We show that for any given positive constant , there exists a polynomial-time approximation algorithmwith an asymptotic worst-case performance ratio of no more than 1 + .