Core Concepts
The authors design and analyze online algorithms for the bin packing problem that leverage frequency predictions about the item sizes in the input sequence. The algorithms aim to achieve a good tradeoff between consistency (competitive ratio with perfect predictions) and robustness (competitive ratio under adversarial prediction error).
Abstract
The content discusses the online bin packing problem, where a sequence of items of various sizes must be packed into a minimum number of bins of uniform capacity. The authors focus on the setting where the online algorithm has access to predictions about the frequency of item sizes in the input sequence.
Key highlights:
The authors present an algorithm called PROFILEPACKING that achieves optimal consistency (competitive ratio with perfect predictions) and is also efficient if the prediction error is relatively small.
PROFILEPACKING builds on the concept of a "profile set" which serves as an approximation of the expected item sizes in the input sequence based on the frequency predictions.
To handle larger prediction errors, the authors design a more general class of "hybrid" algorithms that combine PROFILEPACKING with a robust online algorithm, offering a better tradeoff between robustness and consistency.
The authors provide a theoretical analysis of the algorithms, showing that the robustness of PROFILEPACKING is near-optimal, and no (1+ε)-consistent algorithm can asymptotically do better.
Extensive experiments on various benchmarks demonstrate that the proposed algorithms outperform known efficient algorithms without predictions.
The authors also discuss applications of their algorithms in the context of virtual machine placement in data centers and in the sampling-based setting for fast offline approximations.