TY - JOUR
T1 - On the minimum corridor connection and other generalized geometrich problems.
AU - Bodlaender, H.L.
AU - Feremans, C.
AU - Grigoriev, A.
AU - Penninkx, E.
AU - Sitters, R.
AU - Wolle, T.
PY - 2009/1/1
Y1 - 2009/1/1
N2 - 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.
AB - 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.
U2 - 10.1016/j.comgeo.2009.05.001
DO - 10.1016/j.comgeo.2009.05.001
M3 - Article
SN - 0925-7721
VL - 42
SP - 939
EP - 951
JO - Computational Geometry-Theory and Applications
JF - Computational Geometry-Theory and Applications
IS - 9
ER -