Geodesic
Construction of the minimal enclosing parallelogram
Diskretnaya Matematika, Tome 2 (1990) no. 4, pp. 72-81

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We consider the problem of constructing a minimal-area parallelogram that contains a given $n$-point set $N$. We give a characterization of locally extremal parallelograms; in the nondegenerate case their number is equal to the number of sides of the convex hull of $N$. This makes it possible to give an algorithm for solving the problem with complexity $O(n\log n)$. We also consider the situation when the convex hull $N$ is known a priori. We indicate a method for transfer from one local extremum to another that makes it possible to lower the estimate of the complexity to $O(n)$. 
@article{DM_1990_2_4_a7,
     author = {A. D. Vainshtein},
     title = {Construction of the minimal enclosing parallelogram},
     journal = {Diskretnaya Matematika},
     pages = {72--81},
     publisher = {mathdoc},
     volume = {2},
     number = {4},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1990_2_4_a7/}
}
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A. D. Vainshtein. Construction of the minimal enclosing parallelogram. Diskretnaya Matematika, Tome 2 (1990) no. 4, pp. 72-81. http://geodesic.mathdoc.fr/item/DM_1990_2_4_a7/