A 54 algorithm for two-dimensional packing

This paper proposes a new algorithm for a two-dimensional packing problem first studied by Baker, Coffman, and Rivest (SIAM J. Comput.9, No. 4(1980), 846–855). In their model, a finite list of rectangles is to be packed into a rectangular bin of finite width but infinite height. The model has applications to certain scheduling and stock-cutting problems. Since the problem of finding an optimal packing is NP-hard, previous work has been directed at finding polynomial approximation algorithms for the problem, i.e., algorithms which come within a constant times the height used by an optimal packing. For the algorithm proposed in this paper, the ratio of the height obtained by the algorithm and the height used by an optimal packing is asymptotically bounded by $\text{5}\text{4}$. This bound is an improvement over the bound of $\text{4}\text{3}$ achieved by the best previous algorithm.