Quadratically constrained quadratic programs on acyclic graphs with   application to power flow
  This paper proves that non-convex quadratically constrained quadratic programs can be solved in polynomial time when their underlying graph is acyclic, provided the constraints satisfy a certain technical condition. When this condition is not satisfied, we propose a heuristic to obtain a feasible point. We demonstrate this approach on optimal power flow problems over radial networks. 
Subhonmesh Bose, Dennice F. Gayme, K. Mani Chandy, Steven H. Low
math.OC