# Lower bounds on the performance of online algorithms for relaxed packing problems

@inproceedings{Balogh2022LowerBO,
title={Lower bounds on the performance of online algorithms for relaxed packing problems},
author={J{\'a}nos Balogh and Gyorgy D'osa and Leah Epstein and Lukasz Je.z},
booktitle={International Workshop on Combinatorial Algorithms},
year={2022}
}
• Published in
International Workshop on…
16 January 2022
• Computer Science
We prove new lower bounds for suitable competitive ratio measures of two relaxed online packing problems: online removable multiple knapsack, and a recently introduced online minimum peak appointment scheduling problem. The high level objective in both problems is to pack arriving items of sizes at most 1 into bins of capacity 1 as efficiently as possible, but the exact formalizations differ. In the appointment scheduling problem, every item has to be assigned to a position, which can be seen…

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This work designs randomized and deterministic algorithms for which the competitive ratio is constant on sequences which the optimal off-line algorithm can pack using at most αn bins, if α is constant and known to the algorithm in advance.
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The design and analysis of the first algorithm of asymptotic competitive ratio strictly below 1.58 is provided and an algorithm AH (Advanced Harmonic) whose asymptic competitive ratio does not exceed 1.5783 is provided.
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This work investigates unrestricted algorithms that have the power of performing admission control on the items, i.e., rejecting items while there is enough space to pack them, versus fairalgorithms that reject an item only when there is not enough space.
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This paper presents the first algorithm that beats the competitive ratio, and shows that the lower-order term is inevitable for deterministic algorithms, by improving their upper bound to $1/(1+\ln(2))-O(1/n)$.
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