Dynamic Bin Packing with Predictions

Abstract

The MinUsageTime Dynamic Bin Packing (DBP) problem aims to minimize the accumulated bin usage time for packing a sequence of items into bins. It is often used to model job dispatching for optimizing the busy time of servers, where the items and bins match the jobs and servers respectively. It is known that the competitiveness of MinUsageTime DBP has tight bounds of Θ(√, log μ) and Θ(μ) in the clairvoyant and non-clairvoyant settings respectively, where μ is the max/min duration ratio of all items. In practice, the information about items' durations (i.e., job lengths) obtained via predictions is usually prone to errors. In this paper, we study the MinUsageTime DBP problem with predictions of items' durations. We find that an existing O(√ log μ)-competitive clairvoyant algorithm, if using predicted durations rather than real durations for packing, does not provide any bounded performance guarantee when the predictions are adversarially bad. We develop a new online algorithm with a competitive ratio of {O(∈2 √ log(∈2 μ)}, O(μ) (where ε is the maximum multiplicative error of prediction among all items), achieving O(√ log μ) consistency (competitiveness under perfect predictions where ∈ = 1) and O(μ) robustness (competitiveness under terrible predictions), both of which are asymptotically optimal.