On the Fault-Tolerant Online Bin Packing Problem

TL;DR

This paper introduces Harmonic-Stretch, an online algorithm for fault-tolerant bin packing that maintains packings during ongoing failures, achieving a better competitive ratio than previous methods.

Contribution

It presents a novel online algorithm for fault-tolerant bin packing with ongoing failures, improving the asymptotic competitive ratio from 2 to 1.75.

Findings

Harmonic-Stretch achieves an asymptotic competitive ratio of at most 1.75.

It outperforms previous algorithms with a ratio of 2.

The algorithm effectively handles failures during the packing process.

Abstract

We study the fault-tolerant variant of the online bin packing problem. Similar to the classic bin packing problem, an online sequence of items of various sizes should be packed into a minimum number of bins of uniform capacity. For applications such as server consolidation, where bins represent servers and items represent jobs of different loads, it is required to maintain fault-tolerant solutions. In a fault-tolerant packing, any job is replicated into f+1 servers, for some integer f > 1, so that the failure of up to f servers does not interrupt service. We build over a practical model introduced by Li and Tang [SPAA 2017] in which each job of load $x$ has a primary replica of load $x$ and $f$ standby replicas, each of load $x/\eta$, where $\eta >1$ is a parameter of the problem. Upon failure of up to $f$ servers, any primary replica in a failed bin should be replaced by one of its standby replicas so that the extra load of the new primary replica does not cause an overflow in its bin. We study a general setting in which bins might fail while the input is still being revealed. Our main contribution is an algorithm, named Harmonic-Stretch, which maintains fault-tolerant packings under this general setting. We prove that Harmonic-Stretch has an asymptotic competitive ratio of at most 1.75. This is an improvement over the best existing asymptotic competitive ratio 2 of an algorithm by Li and Tang [TPDS 2020], which works under a model in which bins fail only after all items are packed.