Improved Online Square-into-Square Packing
Abstract
In this paper, we show an improved bound and new algorithm for the online square-into-square packing problem. This two-dimensional packing problem involves packing an online sequence of squares into a unit square container without any two squares overlapping. The goal is to find the largest area α such that any set of squares with total area α can be packed. We show an algorithm that can pack any set of squares with total area α ≤ 3/8 into a unit square in an online setting, improving the previous bound of 11/32.
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