Efficient gabriel graph generation wthout DT

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I need to construct Gabriel Graph. I know an algoritm that uses Delaunay Trinagulation but it's problematic to use because i work with high dimensions. Is there another rather efficient algorithm? It's also acceptable for me to construct an approximation of Gabrial Graph

I tried to check for belonging to the sphere only knns of pairs of nodes which form the sphere but it was too ineficcient for me

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