### Abstract

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.

Original language | English |
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Pages (from-to) | 939-951 |

Number of pages | 12 |

Journal | Computational Geometry-Theory and Applications |

Volume | 42 |

Issue number | 9 |

DOIs | |

Publication status | Published - 1 Jan 2009 |

## Cite this

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