Bin packing is a well studied problem involved in many applications. The classical bin packing problem is about minimising the number of bins and ignores how the bins are utilised. We focus in this paper, on a variant of bin packing that is at the heart of efficient management of data centres. In this context, servers can be viewed as bins and virtual machines as items. The efficient management...

itself is the grand coalition. Usually, the value v(S) is taken to represent the gain that coalition S can achieve if all its members cooperate. A usual goal in the cooperative game is to allocate the total gain v(N) among the individual players in a \fair" way.

Joseph Y.-T. Leung New Jersey Institute of Technology 33.

Bin packing is a well studied problem which has many applications. In this paper we design a robust APTAS for the problem. The robust APTAS receives a single input item to be added to the packing at each step. It maintains an approximate solution throughout this process, by slightly adjusting the solution for each new item. At each step, the total size of items which may migrate between bins mu...

We show a new algorithm and improved bound for the online square-into-square packing problem using a hybrid shelf-packing approach. This 2-dimensional packing problem involves packing an online sequence of squares into a unit square container without any two squares overlapping. We seek the largest area α such that any set of squares with total area at most α can be packed. We show an algorithm...

Summary . The bin packing problem is a fundamental and important optimization in theoretical computer science [4], [6]. An instance sequence of items, each being positive size at most one. task to place all the items into bins so that total one number contain least item minimum. Approximation algorithms have been intensively studied. Algorithm NextFit would be simplest algorithm repeatedly does...