Heuristics for the 0–1 min-knapsack problem
Acta Cybernetica
Randomized algorithms
Stochastic on-line knapsack problems
Mathematical Programming: Series A and B
Searching in an unknown environment: an optimal randomized algorithm for the cow-path problem
Information and Computation
Average-case analysis of off-line and on-line knapsack problems
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Removable Online Knapsack Problems
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
An Online Partially Fractional Knapsack Problem
ISPAN '05 Proceedings of the 8th International Symposium on Parallel Architectures,Algorithms and Networks
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
Finite-State online algorithms and their automated competitive analysis
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Approximate minimization algorithms for the 0/1 Knapsack and Subset-Sum Problem
Operations Research Letters
Online Knapsack Problems with Limited Cuts
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Theoretical Computer Science
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In this paper, we address the online minimization knapsack problem, i. e., the items are given one by one over time and the goal is to minimize the total cost of items that covers a knapsack. We study the removable model, where it is allowed to remove old items from the knapsack in order to accept a new item. We obtain the following results. We propose an 8-competitive deterministic and memoryless algorithm for the problem, which contrasts to the result for the online maximization knapsack problem that no online algorithm has a bounded competitive ratio [8]. We propose a 2e-competitive randomized algorithm for the problem. We derive a lower bound 2 for deterministic algorithms for the problem. We propose a 1.618-competitive deterministic algorithm for the case in which each item has its size equal to its cost, and show that this is best possible.