Approximation algorithms for combinatorial fractional programming problems
Mathematical Programming: Series A and B
A fully polynomial time approximation scheme for minimum cost-reliability ratio problems
Discrete Applied Mathematics
New scaling algorithms for the assignment and minimum mean cycle problems
Mathematical Programming: Series A and B
Biconnectivity approximations and graph carvings
Journal of the ACM (JACM)
An algorithm for fractional assignment problems
Discrete Applied Mathematics - Special issue: Fifth Franco-Japanese Days, Kyoto, October 1992
Efficient algorithms for optimum cycle mean and optimum cost to time ratio problems
Proceedings of the 36th annual ACM/IEEE Design Automation Conference
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A primal-dual schema based approximation algorithm for the element connectivity problem
Journal of Algorithms
The Complexity of Minimum Ratio Spanning Tree Problems
Journal of Global Optimization
Newton's method for fractional combinatorial optimization
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Faster maximum and minimum mean cycle algorithms for system-performance analysis
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Approximation algorithms for fractional knapsack problems
Operations Research Letters
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In the late seventies, Megiddo proposed a way to use an algorithm for the problem of minimizing a linear function a0+a1x1+⋯+anxn subject to certain constraints to solve the problem of minimizing a rational function of the form (a0+a1x1+⋯+anxn)/(b0+b1x1+⋯+bnxn) subject to the same set of constraints, assuming that the denominator is always positive. Using a rather strong assumption, Hashizume et al. extended Megiddo's result to include approximation algorithms. Their assumption essentially asks for the existence of good approximation algorithms for optimization problems with possibly negative coefficients in the (linear) objective function, which is rather unusual for most combinatorial problems. In this paper, we present an alternative extension of Megiddo's result for approximations that avoids this issue and applies to a large class of optimization problems. Specifically, we show that, if there is an α-approximation for the problem of minimizing a nonnegative linear function subject to constraints satisfying a certain increasing property then there is an α-approximation (1/α-approximation) for the problem of minimizing (maximizing) a nonnegative rational function subject to the same constraints. Our framework applies to covering problems and network design problems, among others