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Spanning and splitting: Integer semidefinite programming for the quadratic minimum spanning tree problem

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  • de Meijer, Frank
  • Siebenhofer, Melanie
  • Sotirov, Renata
  • Wiegele, Angelika

Abstract

In the quadratic minimum spanning tree problem (QMSTP) one wants to find the minimizer of a quadratic function over all possible spanning trees of a graph. We present a formulation of the QMSTP as a mixed-integer semidefinite program exploiting the algebraic connectivity of a graph. Based on this formulation, we derive a doubly nonnegative relaxation for the QMSTP and investigate classes of valid inequalities to strengthen the relaxation using the Chvátal-Gomory procedure for mixed-integer conic programming.

Suggested Citation

  • de Meijer, Frank & Siebenhofer, Melanie & Sotirov, Renata & Wiegele, Angelika, 2026. "Spanning and splitting: Integer semidefinite programming for the quadratic minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 331(2), pages 381-395.
    • Handle: RePEc:eee:ejores:v:331:y:2026:i:2:p:381-395
    DOI: 10.1016/j.ejor.2025.10.051
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