Bin packing with fragmentable items: Presentation and approximations

We consider a variant of the Bin Packing Problem dealing with fragmentable items. Given a fixed number of bins, the objective is to put all the items into the bins by splitting them in a minimum number of fragments. This problem is useful for modeling splittable resource allocation. In this paper we introduce the problem and its complexity. We give and prove several properties then we present various approximation algorithms and specially a 65-approximation algorithm.