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A note on the monotonicity of pseudo-Boolean functions

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Summary

RecentlyWilde andSanchez-Anton [1971] have studied monotonically increasing pseudo-Boolean functions, and have given a very efficient method for their minimization. The role of this note is to give an equivalent formulation of this property and to show how the new formulation makes it possible to read the sought minimum directly from the expression of the given function.

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References

  • Hammer, P. L., andS. Rudeanu: Boolean Methods in Operations Research and Related Areas. Springer Verlag, Berlin-Heidelberg-New York, 1968 and Dunod, Paris 1970.

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  • Wilde, D. J., andJ. M. Sanchez-Anton: Discrete Optimization on a Multivariable Boolean Lattice. Mathematical Programming1, 301–306, 1971.

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Authors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada

    P. L. Hammer

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  1. P. L. Hammer
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Additional information

Work partially supported by the National Research Council Grant A 8552.

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Hammer, P.L. A note on the monotonicity of pseudo-Boolean functions. Zeitschrift für Operations Research 18, 47–50 (1974). https://doi.org/10.1007/BF01949713

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  • DOI: https://doi.org/10.1007/BF01949713

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