Optimal Nearly-Similar Polygon Stabbers of Convex Polygons

A convex polygon that is nearly-similar to a model polygon P has sides parallel and in the same order to the corresponding sides of P. The lengths of the sides are unrestricted and may be zero. Given a set of target convex polygons in the plane with a total of n vertices, and a xed model convex stabbing polygon P, the minimum-perimeter polygon nearly-similar to P that stabs the targets can be found in time O(n) (but time exponential in the number of sides in the stabbing polygon).