Cutting out Polygons with Lines and Rays

Abstract

We present approximation algorithms for cutting out polygons with line cuts and ray cuts Our results answer a number of open problems and are either the first solutions or significantly improve over previously known solutions For the line cutting version, we prove a key property that leads to a simple, constant factor approximation algorithm For the ray cutting version, we prove it is possible to compute in almost linear time a cutting sequence that is an O(log2n)-factor approximation No algorithms were previously known for the ray cutting version.