Fully-Dynamic Bin Packing with Limited Repacking

Abstract

We study the classic Bin Packing problem in a fully-dynamic setting, where new items can arrive and old items may depart. We want algorithms with low asymptotic competitive ratio \emph{while repacking items sparingly} between updates. Formally, each item $i$ has a \emph{movement cost} $c_i\geq 0$, and we want to use $\alpha \cdot OPT$ bins and incur a movement cost $\gamma\cdot c_i$, either in the worst case, or in an amortized sense, for $\alpha, \gamma$ as small as possible. We call $\gamma$ the \emph{recourse} of the algorithm. This is motivated by cloud storage applications, where fully-dynamic Bin Packing models the problem of data backup to minimize the number of disks used, as well as communication incurred in moving file backups between disks. Since the set of files changes over time, we could recompute a solution periodically from scratch, but this would give a high number of disk rewrites, incurring a high energy cost and possible wear and tear of the disks. In this work, we present optimal tradeoffs between number of bins used and number of items repacked, as well as natural extensions of the latter measure.