Approximation algorithms for cutting out polygons with lines and rays

Abstract

This paper studies the problem of cutting out a given polygon, drawn on a convex piece of paper, in the cheapest possible way. For the problems of cutting out convex polygons with line cuts and ray cuts, we present a 7.9-approximation algorithm and a 6-approximation algorithm, respectively. For the problem of cutting out ray-cuttable polygons, an O(log n)-approximation algorithm is given. © Springer-Verlag Berlin Heidelberg 2005.