Approximation algorithms for combinatorial fractional programming problems
Mathematical Programming: Series A and B
Hyperbolic 0-1 programming and query optimization in information retrieval
Mathematical Programming: Series A and B
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
An approximate dynamic programming approach to convex quadratic knapsack problems
Computers and Operations Research
An approximate dynamic programming approach to convex quadratic knapsack problems
Computers and Operations Research
Approximating rational objectives is as easy as approximating linear ones
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Polynomial-Time approximation schemes for shortest path with alternatives
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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We consider the combinatorial optimization problem where the objective function is the ratio of two linear functions. This type of problems can be solved by an algorithm that uses an auxiliary problem with a parametrized linear objective function. We propose for the original problem an approximation scheme based on the one hand upon an approximation scheme for the auxiliary problem and on the other hand upon a constant approximation algorithm for the original problem. As an example of the method we propose an O(n^2) time 12-approximation algorithm for the fractional 0-1 knapsack problem (BFKP) which combined with a known approximation scheme for the 0-1 linear knapsack problem running in O(n^3/@e) leads to a fully polynomial-time approximation scheme (FPTAS) for BFKP with time complexity O(n^3/@e). In the same way we propose a FPTAS for the unbounded fractional knapsack problem with time complexity O(n^2+nlog(1/@e)+(1/@e)^3).