Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
A New Fully Polynomial Approximation Scheme for the Knapsack Problem
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
Hybrid Rounding Techniques for Knapsack Problems
Hybrid Rounding Techniques for Knapsack Problems
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We address the classical knapsack problem and a variant in which an upper bound is imposed on the number of items that can be selected. We show that appropriate combinations of rounding techniques yield novel and more powerful ways of rounding. Moreover, we present a linear-storage polynomial time approximation scheme (PTAS) and a fully polynomial time approximation scheme (FPTAS) that compute an approximate solution, of any fixed accuracy, in linear time. These linear complexity bounds give a substantial improvement of the best previously known polynomial bounds [A. Caprara, et al., Approximation algorithms for knapsack problems with cardinality constraints, European J. Oper. Res. 123 (2000) 333-345].