On Guillotine Cutting Sequences

Imagine a wooden plate with a set of non-overlapping geometric objects painted on it. How many of them can a carpenter cut out using a panel saw making guillotine cuts, i.e., only moving forward through the material along a straight line until it is split into two pieces? Already fifteen years ago, Pach and Tardos investigated whether one can always cut out a constant fraction if all objects are axis-parallel rectangles. However, even for the case of axis-parallel squares this question is still open. In this paper, we answer the latter affirmatively. Our result is constructive and holds even in a more general setting where the squares have weights and the goal is to save as much weight as possible. We further show that when solving the more general question for rectangles affirmatively with only axis-parallel cuts, this would yield a combinatorial O(1)approximation algorithm for the Maximum Independent Set of Rectangles problem, and would thus solve a long-standing open problem. In p...

• Type: Journal
• Year: 2015
• Where: APPROX
• Authors: Fidaa Abed, Parinya Chalermsook, José R. Correa, Andreas Karrenbauer, Pablo Pérez-Lantero, José A. Soto, Andreas Wiese
• Keywords: Algorithms, APPROX 2015