The potato-peeling problem asks for the largest convex polygon contained inside a given simple polygon. We give an O(n 7) time algorithm to this problem, answering a question of Goodman. We also give an O(n 6) time algorithm if the desired polygon is maximized with respect to perimeter.

We show that the smallest k-gon circumscribing a convex n-gon can be computed in O (n z log n log k) time.

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Given a set of n points on the plane, the rectilinear m-center problem is to find n rectilinear squares covering all these n points such that the maximum side length of these squares is minimized. In this paper we prove that there is no polynomial-time algorithm with an error ratio e < 2 for the rectilinear m-center problem unless NP= P. A polynomial-time approximation algorithm with an error ratio of 2 is also proposed.