Adaptive Bin Packing with Overflow
Sebastian Perez-Salazar, Mohit Singh, Alejandro Toriello

TL;DR
This paper introduces an online algorithm for adaptive bin packing with overflow, minimizing total costs by balancing bin usage and overflow penalties, applicable to cloud resource management with probabilistic item sizes.
Contribution
It develops an online algorithm with provable performance guarantees and a PTAS for the offline problem, addressing unknown and known distributions respectively.
Findings
Online algorithm achieves constant-factor approximation.
PTAS provides near-optimal solutions for offline packing.
Empirical results demonstrate effective performance of the online method.
Abstract
Motivated by bursty bandwidth allocation and by the allocation of virtual machines to servers in the cloud, we consider the online problem of packing items with random sizes into unit-capacity bins. Items arrive sequentially, but upon arrival an item's actual size is unknown; only its probabilistic information is available to the decision maker. Without knowing this size, the decision maker must irrevocably pack the item into an available bin or place it in a new bin. Once packed in a bin, the decision maker observes the item's actual size, and overflowing the bin is a possibility. An overflow incurs a large penalty cost and the corresponding bin is unusable for the rest of the process. In practical terms, this overflow models delayed services, failure of servers, and/or loss of end-user goodwill. The objective is to minimize the total expected cost given by the sum of the number of…
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