The cost of cutting out convex n-gons Original Research Article

Given a convex n-gon P drawn on a piece of paper Q of unit diameter we prove that it can be cut with a total cost of O(log n). This bound is shown to be asymptotically tight: a regular n-gon (whose circumscribed circle has radius, say, 1/3) drawn on a square piece of paper of unit diameter requires a cut cost of Ω(log n).