Hyperbolic 0-1 programming and query optimization in information retrieval
Mathematical Programming: Series A and B
Optimizing the sum of linear fractional functions
Recent advances in global optimization
Fault Management in Distributed Systems: A Policy-Driven Approach
Journal of Network and Systems Management
Approximating rational objectives is as easy as approximating linear ones
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
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We examine the complexity of two minimum spanning tree problems with rational objective functions. We show that the Minimum Ratio Spanning Tree problem is NP-hard when the denominator is unrestricted in sign, thereby sharpening a previous complexity result. We then consider an extension of this problem where the objective function is the sum of two linear ratios whose numerators and denominators are strictly positive. This problem is shown to be NP-hard as well. We conclude with some results characterizing sufficient conditions for a globally optimal solution.