Base Location Problems for Base-Monotone Regions
The problem of decomposing a pixel grid into base-monotone regions was first studied in the context of image segmentation. It is known that for a given pixel grid and baselines, one can compute in polynomial time a maximum-weight region that can be decomposed into disjoint base-monotone regions [Chun et al. ISAAC 2009]. We continue this line of research and show the NP-hardness of the problem of optimally locating k baselines in a given n ×n pixel grid. We also present an O(n 3)-time 2-approximation algorithm for this problem. We then study two related problems, the k base-segment problem and the quad-decomposition problem, and present some complexity results for them.
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