Complexity of finding a spanning tree that minimizes the maximum interference
This problem already is known, and is NP-Hard, but if you like to know more about the interference related problems I'd offer you to read this book.

The Problem 1, in the Buchin work is as follow:


  Problem 1 (Locher, von Rickenbach, Wattenhofer[5]). Given n nodes in
  the plane. Connect the nodes by a spanning tree. For each node v we
  construct a disk centering at v with radius equal to the distance to
  v's furthest neighbor in the spanning tree. The interference of a node
  v is then defined as the number of disks that include node v (not
  counting the disk of v itself ). Find a spanning tree that minimizes
  the maximum interference.