Engineering Branch-and-Cut Algorithms for the Equicut Problem

Part of the Fields Institute Communications book series (FIC, volume 69)


A minimum equicut of an edge-weighted graph is a partition of the nodes of the graph into two sets of equal size such that the sum of the weights of edges joining nodes in different partitions is minimum. We compare basic linear and semidefinite relaxations for the equicut problem, and find that linear bounds are competitive with the corresponding semidefinite ones but can be computed much faster. Motivated by an application of equicut in theoretical physics, we revisit an approach by Brunetta et al. and present an enhanced branch-and-cut algorithm. Our computational results suggest that the proposed branch-and-cut algorithm has a better performance than the algorithm of Brunetta et al. Further, it is able to solve to optimality in reasonable time several instances with more than 200 nodes from the physics application.

Key words

Equicut Maximum-Cut Bisection Graph partitioning Linear programming Semidefinite programming Branch-and-cut 

Subject Classifications

90C57 90C22 90C05 90C27 



Financial support from the German Science Foundation is acknowledged under contract Li 1675/1. The first author acknowledges financial support from the Alexander von Humboldt Foundation and from the Natural Science and Engineering Research Council of Canada. We thank Helmut G. Katzgraber, Creighton Thomas and Juan Carlos Andersen for providing us with instances for the physics application.


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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  1. 1.Canada Research Chair in Discrete Nonlinear Optimization in EngineeringGERAD & École Polytechnique de MontréalMontrealCanada
  2. 2.Department MathematikFriedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany
  3. 3.Institut für InformatikUniversität zu KölnKölnGermany

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