Balanced Circle Packings for Planar Graphs
  We study balanced circle packings and circle-contact representations for planar graphs, where the ratio of the largest circle's diameter to the smallest circle's diameter is polynomial in the number of circles. We provide a number of positive and negative results for the existence of such balanced configurations. 
Md. Jawaherul Alam, David Eppstein, Michael T. Goodrich, Stephen G.   Kobourov, and Sergey Pupyrev
cs.CG