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}
}
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… 

References

SHOWING 1-10 OF 21 REFERENCES

The Competitive Ratio for On-Line Dual Bin Packing with Restricted Input Sequences

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.

A new and improved algorithm for online bin packing

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.

Fair versus Unrestricted Bin Packing

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.

An Optimal Algorithm for Online Multiple Knapsack

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 $1/(1+\ln(2))-O(1/n)$.

Online Knapsack Revisited

We investigate the online variant of the (Multiple) Knapsack Problem: an algorithm is to pack items, of arbitrary sizes and profits, in k knapsacks (bins) without exceeding the capacity of any bin.

Improved lower bounds for the online bin packing problem with cardinality constraints

A new method to derive lower bounds for general $$k$$k and present improved bounds for various cases of k = 4$$k≥4 and k = 5$$k=5 is proposed.

Approximation Algorithms for Demand Strip Packing

The main result is a (5/3 + ε)approximation algorithm for any constant ε > 0.5, which achieves best-possible approximation factors for some relevant special cases.

Scheduling Appointments Online: The Power of Deferred Decision-Making

How deferred decision-making can be leveraged to yield improved worst-case performance is demonstrated, and the first known lower bound of 1.2 on the asymptotic competitive ratio of both deterministic and randomized online MPAS algorithm is presented.

New Lower Bounds for Certain Classes of Bin Packing Algorithms

A New Lower Bound for Classic Online Bin Packing

The advantage of branching and the applicability of full adaptivity in the design of lower bounds for the classic online bin packing problem are demonstrated and a new method for weight based analysis is applied, usually applied only in proofs of upper bounds.