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We consider a variant of the classical Bin Packing Problem, called FullyDynamic Bin Packing. In this variant, items of a size in $(0,1]$ must be packedin bins of unit size. In each time step, an item either arrives or departs fromthe packing. An algorithm for this problem must maintain a feasible packingwhile only repacking a bounded number of items in each time step.  We develop an algorithm which repacks only a constant number of items pertime step and, unlike previous work, does not rely on bundling of small itemswhich allowed those solutions to move an unbounded number of small items asone. Our algorithm has an asymptotic approximation ratio of roughly $1.3871$which is complemented by a lower bound of Balogh et al., resulting in a tightapproximation ratio for this problem. As a direct corollary, we also close thegap to the lower bound of the Relaxed Online Bin Packing Problem in which onlyinsertions of items occur.

A Tight Approximation for Fully Dynamic Bin Packing without Bundling