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The Complexity of Minimum Ratio Spanning Tree Problems

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Abstract

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.

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Authors and Affiliations

  1. Lion Technologies, Inc., 1921 Thurston Road, Comus, MD, 20842, USA

    Christopher C. Skiścim

  2. Information Technology and Management Science Program, James Madison University, Harrisonburg, VA, 22087, USA

    Susan W. Palocsay

Authors
  1. Christopher C. Skiścim
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  2. Susan W. Palocsay
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Skiścim, C.C., Palocsay, S.W. The Complexity of Minimum Ratio Spanning Tree Problems. J Glob Optim 30, 335–346 (2004). https://doi.org/10.1007/s10898-004-5119-8

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  • DOI: https://doi.org/10.1007/s10898-004-5119-8

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