An optimal algorithm for one-separation of a set of isothetic polygons
We consider the problem of separating a collection of isothetic polygons in the plane by translating one polygon at a time to infinity. The directions of translation are the four isothetic (parallel to the axes) directions, but a particular polygon can be translated only in one of these four directions. Our algorithm detects whether a set is separable in this sense and computes a translational ordering of the polygons. The time and space complexities of our algorithm is Θ(n log n) and Θ(n) respectively, where n is the total number of edges of the polygons in the set. The best previous algorithm in the plane for this problem had complexities of O(n log2n) time and O(n log n) space.
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