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We consider schemes for recursively dividing a set of geometric objects by hyperplanes until all objects are separated. Such a binary space partition, or BSP, is naturally considered as a binary tree where each internal node corresponds to a division. The goal is to choose the hyperplanes properly so that the size of the BSP, i.e., the number of resulting fragments of the objects, is minimized. For the twodimensional case, we construct BSPs of size O(n log n) for n edges, while in threedoi:10.1007/bf02187806 fatcat:lv6gjvjmxnaxvf7xayvicgcrri