Bidirected minimum Manhattan network problem

In the bidirected minimum Manhattan network problem, given a set T of n terminals in the plane, no two terminals on the same horizontal or vertical line, we need to construct a network N(T) of minimum total length with the property that the edges of N(T) belong to the axis‐parallel grid defined by T and are oriented in a such a way that every ordered pair of terminals is connected in N(T) by a directed Manhattan path. In this article, we present a polynomial factor 2‐approximation algorithm for the bidirected minimum Manhattan network problem.