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 an subexponential time exact algorithm. For the special case of k-outerplanar graphs the running time becomes O(n 3). 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.
This work was supported by the Netherlands Organisation for Scientific Research NWO (project Treewidth and Combinatorial Optimisation).
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Bodlaender, H., Feremans, C., Grigoriev, A., Penninkx, E., Sitters, R., Wolle, T. (2007). On the Minimum Corridor Connection Problem and Other Generalized Geometric Problems. In: Erlebach, T., Kaklamanis, C. (eds) Approximation and Online Algorithms. WAOA 2006. Lecture Notes in Computer Science, vol 4368. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11970125_6
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DOI: https://doi.org/10.1007/11970125_6
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