A Polynomial Solution for Potato-peeling

We give a finiteness criteria for the potato-peeling p b l m that asks for the largest convex polygon (‘potato’) contained inside a given simple polygon, answering a question of J. Goodman. This leads to a polynomial-time solution of O(n91og M ) . The techniques used turn out to be useful for other cases of what we call the polygon incluswn and enclosure problem. For instance, the largest perimeter potato can be found in O(n6) time and finding the Smallest k-gon dos ing a given