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 n ⇥ n pixel grid and baselines, one can compute in O(n) time a maximum-weight region that can be decomposed into disjoint base-monotone regions [Chun et al. ISAAC 2009]. To complement this fact, we first show the NP-hardness of the problem of optimally locating k baselines in a given pixel grid. Next we present an O(n)time 2-approximation algorithm for this problem. We also study some polynomial-time solvable cases, and variants of the problem.