Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Scheduling with forbidden sets
Discrete Applied Mathematics - Special issue on models and algorithms for planning and scheduling problems
Approximate Algorithms for the 0/1 Knapsack Problem
Journal of the ACM (JACM)
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the hardness of reoptimization
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Reoptimization of the maximum weighted Pk-free subgraph problem under vertex insertion
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
Reoptimization of some maximum weight induced hereditary subgraph problems
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
A theory and algorithms for combinatorial reoptimization
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Reoptimization of the minimum total flow-time scheduling problem
MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms
Reoptimizing the rural postman problem
Computers and Operations Research
Reallocation problems in scheduling
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
Reoptimization of maximum weight induced hereditary subgraph problems
Theoretical Computer Science
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In this paper we study the problem where an optimal solution of a knapsack problem on n items is known and a very small number k of new items arrive. The objective is to find an optimal solution of the knapsack problem with n+k items, given an optimal solution on the n items (reoptimization of the knapsack problem). We show that this problem, even in the case k=1, is NP-hard and that, in order to have effective heuristics, it is necessary to consider not only the items included in the previously optimal solution and the new items, but also the discarded items. Then, we design a general algorithm that makes use, for the solution of a subproblem, of an @a-approximation algorithm known for the knapsack problem. We prove that this algorithm has a worst-case performance bound of 12-@a, which is always greater than @a, and therefore that this algorithm always outperforms the corresponding @a-approximation algorithm applied from scratch on the n+k items. We show that this bound is tight when the classical Ext-Greedy algorithm and the G^3^4 algorithm are used to solve the subproblem. We also show that there exist classes of instances on which the running time of the reoptimization algorithm is smaller than the running time of an equivalent PTAS and FPTAS.