On-line grid-packing with a single active grid

Abstract

In this paper, we study the problem of packing rectangular items into a minimum number of square grids in an on-line manner with a single active grid, where the size of each grid is m × m for some positive integer m, and the height and the width of each item are positive integers smaller than or equal to m, respectively. We first prove that the asymptotic competitive ratio of an optimal on-line algorithm is at least 23/ 11. We then propose an on-line algorithm that achieves a competitive ratio O((log logm)2).