Please consider the following problem:


Given: a simple graph (without self-loops and without multiple edges) $G$ on $n$ vertices. 


Task: place equidistantly the vertices of $G$ on a circle of unit radius and draw the edges of $G$ in such a way that their total length is minimized. 


What is the complexity of this problem? 


What is the relevant literature?



Drawing graphs on circles
As S. Carnahan and Kristal Cantwell mentions it in the comments, this problem is NP-hard. See:


Rubber bands, convex embeddings and graph connectivity by N. Linial, L. Lovász and A. Wigderson


