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 -