Optimal Resource Augmentations for Online Knapsack
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Selling ad campaigns: online algorithms with cancellations
Proceedings of the 10th ACM conference on Electronic commerce
Online Knapsack Problems with Limited Cuts
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Online knapsack with resource augmentation
Information Processing Letters
Online removable knapsack with limited cuts
Theoretical Computer Science
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Online minimization knapsack problem
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
Theoretical Computer Science
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The knapsack problem can and has been used to model many resource sharing problems. The allocation of a portion of a resource to a particular agent provides a benefit to the system, but also blocks other agents from utilizing that portion of the resource. For a problem where the number of agents as well as each agent's demand and potential benefit are known prior to any decision being made, the optimal allocation and its value can be calculated. In many situations these values are not known initially, but only learned over time. Online algorithms and competitive analysis are often employed when a problem requires decisions to be made prior to having all information available. In this paper we will suggest an online version of the knapsack problem, provide some justification for the model, give the exact competitive ratio for the problem in the deterministic case, and provide bounds on the competitive ratio in the randomized case.