Guillotine cuts

Abstract

In guillotine cut problem, we are given non-intersecting convex sets in the plane and we are allowed straight line cuts. If a cut passes through an object, it kills that object. Can one always save a constant fraction or Ω(n) objects? For the general case, Pach and Tardos answered in the negative. We investigate the case where we have axis-parallel rectangles and only horizontal and vertical guillotine cuts are allowed. Ω(n) bound here would have interesting implications for the Maximum Independent Set of Rectangles problem - it would imply a constant factor or O(1) approximation for it. Unable to solve the problem in its totality, we discuss some approaches and small results.