Abstract:The computation of the minimum-volume bounding box of a point set in R 3 is a hard problem. The best known exact algorithm requires O(n 3) time, so several approximation algorithms and heuristics are preferred in practice. Among them, the algorithm based on PCA (Principal Component Analysis) plays an important role. Recently, it has been shown that the discrete PCA algorithm may fail to approximate the minimum-volume bounding box even for a large constant factor. Moreover, this happens only for some very speci… Show more
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