We consider the problem of removing c points from a set S of n points so that the remaining point set is optimal in some sense. Definitions of optimality we consider include having minimum diameter, having minimum area (perimeter) bounding box, having minimum area (perimeter) convex hull. For constant values of c, all our algorithms run in O (n log n) time.

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doi.org/10.1016/j.jda.2008.12.002
Journal of Discrete Algorithms
School of Computer Science

Atanassov, R. (Rossen), Bose, P, Couture, M. (Mathieu), Maheshwari, A, Morin, P, Paquette, M. (Michel), … Wuhrer, S. (Stefanie). (2009). Algorithms for optimal outlier removal. Journal of Discrete Algorithms, 7(2), 239–248. doi:10.1016/j.jda.2008.12.002