A simple proof of Liang's lower bound for on-line bin packing and the extension to the parametric case

In this note we present a simplified proof of a lower bound for on-line bin packing. This proof also covers the well-known result given by Liang in Inform. Process Lett. 10 (1980) 76–79.

A simple proof of Liang's lower bound for on-line bin packing and the extension to the parametric case

In this note we present a simplified proof of a lower bound for on-line bin packing. This proof also covers the well-known result given by Liang in Inform. Process Lett. 10 (1980) 76–79

Two-dimensional rectangle packing: on-line methods and results

The first algorithms for the on-line two-dimensional rectangle packing problem were introduced by Coppersmith and Raghavan. They showed that for a family of heuristics 13/4 is an upper bound for the asymptotic worst-case ratios. We have investigated the Next Fit and the First Fit variants of their method. We proved that the asymptotic worst-case ratio equals 13/4 for the Next Fit variant and that 49/16 is an upper bound of the asymptotic worst-case ratio for the First Fit variant.

Lower bounds for several online variants of bin packing

We consider several previously studied online variants of bin packing and prove new and improved lower bounds on the asymptotic competitive ratios for them. For that, we use a method of fully adaptive constructions. In particular, we improve the lower bound for the asymptotic competitive ratio of online square packing significantly, raising it from roughly 1.68 to above 1.75.Comment: WAOA 201

Lower bounds for 1-, 2- and 3-dimensional on-line bin packing algorithms

In this paper we discuss lower bounds for the asymptotic worst case ratio of on-line algorithms for different kind of bin packing problems. Recently, Galambos and Frenk gave a simple proof of the 1.536 ... lower bound for the 1-dimensional bin packing problem. Following their ideas, we present a general technique that can be used to derive lower bounds for other bin packing problems as well. We apply this technique to prove new lower bounds for the 2-dimensional (1.802...) and 3-dimensional (1.974...) bin packing problem