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A generalized version of this problem is to find a minimum cost <math>S</math> for a given cost function.
The brother of this problem where one looks for a minimum cardinality set of nodes to pin so as to render <math>G+K_S</math> infinitesimally rigid was solved by
Tibor JordanJordán<ref>Jordan, T. Jordán, ''Rigid and Globally Rigid Graphs with Pinned Vertices'', [http://www.cs.elte.hu/egres/tr/egres-09-05.pdfEGRES Technical Report No. 2009-05].</ref>. In that same paper an approximation algorithm is given to finding the pinning set to achieve global rigidity. An approximation factor of 5/2 is proven also for the cost version.
