Graph bisection revisited

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Abstract

The graph bisection problem is the problem of partitioning the vertex set of a graph into two sets of given sizes such that the sum of weights of edges joining these two sets is optimized. We present a semidefinite programming relaxation for the graph bisection problem with a matrix variable of order n—the number of vertices of the graph—that is equivalent to the currently strongest semidefinite programming relaxation obtained by using vector lifting. The reduction in the size of the matrix variable enables us to impose additional valid inequalities to the relaxation in order to further strengthen it. The numerical results confirm that our simplified and strengthened semidefinite relaxation provides the currently strongest bound for the graph bisection problem in reasonable time.
Original languageEnglish
Pages (from-to)143-154
JournalAnnals of Operations Research
Volume265
Issue number1
DOIs
Publication statusPublished - Jun 2018

Keywords

  • graph bisection
  • graph partition
  • semidefinite programming
  • boolean quadratic polytope

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