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Maximum Cut Problem, MAX-CUT

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Encyclopedia of Optimization

Article Outline

Introduction

  Organization

  Idiosyncrasies

Formulation

Methods

  Review of Solution Approaches

  C-GRASP Heuristic

Conclusions

See also

References

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Notes

  1. 1.

    Notice that the result holds even if (without the loss of generality) \( { V_{1} = V } \) and \( { V_{2} = \emptyset } \). In this case, a cut induced by \( { (V_{1},V_{2}) } \) will be a maximum cut if \( { w_{ij} \le 0, \quad\forall i,j \in V } \).

  2. 2.

    This is the “typical” definition of a  Uniform distribution. That is, \( { P\,\colon X \mapsto \mathbb{R} } \) is uniform onto [A,B), if, for any subinterval \( { I \subset [A,B) } \), the measure of P −1(I) equals the length of I.

  3. 3.

    uniformly at random

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Author information

Authors and Affiliations

  1. Air Force Research Laboratory, Munitions Directorate, and Dept. of Industrial and Systems Engineering, University of Florida, Gainesville, USA

    Clayton W. Commander

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  1. Clayton W. Commander
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Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544-5263, USA

    Christodoulos A. Floudas

  2. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611-6595, USA

    Panos M. Pardalos

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© 2008 Springer-Verlag

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Commander, C. (2008). Maximum Cut Problem, MAX-CUT . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_358

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