Linear-time heuristics for minimum weight rectangulation
We consider the problem of partitioning rectilinear polygons into rectangles, using segments of minimum total length. This problem is NP-hard for polygons with holes. Even for hole-free polygons no known algorithm can find an optimal partitioning in less than O(n4) time.
We present the first linear-time algorithm for computing rectangulations of hole-free polygons, within a constant factor of the optimum. We achieve this result by deriving a linear-time algorithm for producing rectangulations of histograms of length less than 2.42 times the optimum, and then solving the problem of producing a proper partition into histograms.
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