In this paper we discuss the complexity and approximability of the minimum corridor connection problem where, given a rectilinear decomposition of a rectilinear polygon into “rooms”, one has to find the minimum length tree along the edges of the decomposition such that every room is incident to a vertex of the tree. We show that the problem is strongly np-hard and give a subexponential time exact algorithm. For the special case when the room connectivity graph is k-outerplanar the algorithm running time becomes cubic. We develop a polynomial time approximation scheme for the case when all rooms are fat and have nearly the same size. When rooms are fat but are of varying size we give a polynomial time constant factor approximation algorithm.
Bodlaender, H. L., Feremans, C., Grigoriev, A., Penninkx, E., Sitters, R., & Wolle, T. (2009). On the minimum corridor connection and other generalized geometrich problems. Computational Geometry-Theory and Applications, 42(9), 939-951. https://doi.org/10.1016/j.comgeo.2009.05.001