Dynamic multi-dimensional bin packing

Competitive Multi-dimensional Dynamic Bin Packing via L-Shape Bin Packing

In this paper, we study the d-dimensional dynamic bin packing problem for general ddimensional boxes, for d ≥ 2. This problem is a generalization of the bin packing problem in which items may arrive and depart dynamically. Our main result is a 3-competitive online algorithm. We further study the 2and 3-dimensional problem closely and improve the competitive ratios. Technically speaking, our d-d...

Online Multi-dimensional Dynamic Bin Packing of Unit-Fraction Items

We study the 2-D and 3-D dynamic bin packing problem, in which items arrive and depart at arbitrary times. The 1-D problem was first studied by Coffman, Garey, and Johnson motivated by the dynamic storage problem. Bar-Noy et al. have studied packing of unit fraction items (i.e., items with length 1/k for some integer k ≥ 1), motivated by the window scheduling problem. In this paper, we extend t...

Multi - Capacity Bin Packing

Multi-dimensional bin packing problems with guillotine constraints

The problem addressed in this paper is the decision problem of determining if a set of multi-dimensional rectangular boxes can be orthogonally packed into a rectangular bin while satisfying the requirement that the packing should be guillotine cuttable. That is, there should exist a series of face parallel straight cuts that can recursively cut the bin into pieces so that each piece contains a ...

Fully Dynamic Bin Packing Revisited

We consider the fully dynamic bin packing problem, where items arrive and depart in an online fashion. The goal is to minimize the number of used bins at every timestep while repacking of already packed items is allowed. Ivković and Lloyd [IL98] have developed an algorithm with asymptotic competitive ratio of 5/4 using O(log n) (amortized) shifting moves whenever an item is inserted or removed ...