A new family of simplicial TSP instances proves unbounded integrality gaps for the de Klerk-Sotirov SDP and all SDP relaxations surveyed in Sotirov [24], while the subtour LP solves them with zero gap.
For the first result, we use the identity d∑ j=1 cos (2πjk n ) =−1 + (−1)k 2 with k = 1
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Semidefinite Programming Relaxations of the Traveling Salesman Problem and Their Integrality Gaps
A new family of simplicial TSP instances proves unbounded integrality gaps for the de Klerk-Sotirov SDP and all SDP relaxations surveyed in Sotirov [24], while the subtour LP solves them with zero gap.