On the finite convergence of the Douglas-Rachford algorithm for solving   (not necessarily convex) feasibility problems in Euclidean spaces
  Solving feasibility problems is a central task in mathematics and the applied sciences. One particularly successful method is the Douglas-Rachford algorithm. In this paper, we provide many new conditions sufficient for finite convergence. Numerous examples illustrate our results. 
Heinz H. Bauschke and Minh N. Dao
math.OC math.FA math.NA