Bidirected minimum Manhattan network problem
  In the bidirected minimum Manhattan network problem, given a set T of n terminals in the plane, we need to construct a network N(T) of minimum total length with the property that the edges of N(T) are axis-parallel and oriented in a such a way that every ordered pair of terminals is connected in N(T) by a directed Manhattan path. In this paper, we present a polynomial factor 2 approximation algorithm for the bidirected minimum Manhattan network problem. 
Nicolas Catusse, Victor Chepoi, Karim Nouioua, Yann Vaxes
cs.CG