On-line bin-packing problem : maximizing the number of unused bins

In this paper, we study the on-line version of the bin-packing problem. We analyze the approximation behavior of an on-line bin-packing algorithm under an approximation criterion called differential ratio. We are interested in two types of results : the differential competitivity ratio guaranteed by the on-line algorithm and hardness results that account for the difficulty of the problem and for the quality of the algorithm developed to solve it. In its off-line version, the bin-packing problem, BP, is better approximated in differential framework than in standard one. Our objective is to determine if or not such result exists for the on-line version of BP.