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On semidefinite programming relaxations of maximum \(k\)-section


We derive a new semidefinite programming bound for the maximum \(k\)-section problem. For \(k=2\) (i.e. for maximum bisection), the new bound is at least as strong as a well-known bound by Poljak and Rendl (SIAM J Optim 5(3):467–487, 1995). For \(k \ge 3\) the new bound dominates a bound of Karisch and Rendl (Topics in semidefinite and interior-point methods, 1998). The new bound is derived from a recent semidefinite programming bound by De Klerk and Sotirov for the more general quadratic assignment problem, but only requires the solution of a much smaller semidefinite program.

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The authors would like to thank Edwin van Dam, Willem Haemers, and René Peters for useful discussions on strongly regular graphs, and for providing several maximum-\(k\)-section instances on these graphs.

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Correspondence to Etienne de Klerk.

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de Klerk, E., Pasechnik, D., Sotirov, R. et al. On semidefinite programming relaxations of maximum \(k\)-section. Math. Program. 136, 253–278 (2012).

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  • Maximum bisection
  • Maximum section
  • Semidefinite programming
  • Coherent configurations
  • Strongly regular graph

Mathematics Subject Classification (2000)

  • 90C22
  • 20Cxx
  • 70-08