Guillotine

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 ar...

Innovation and the Financial Guillotine

We examine how investors’ tolerance for failure impacts the types of projects they are willing to fund. We show that actions that reduce short term accountability and thus encourage agents to experiment more simultaneously reduce the level of experimentation financial backers are willing to fund. Failure tolerance has an equilibrium price that increases in the level of experimentation. More exp...

A Tale on Guillotine Cut

The guillotine cut is an important tool to design polynomialtime approximation schemes for geometric optimization problems. In this article, we survey its history and recent developments.

Further Reflections on the Guillotine

Guillotine Cut in Approximation Algorithms

The guillotine cut is one of main techniques to design polynomial-time approximation schemes for geometric optimization problems. This article is a mini survey on its history and current developments. ∗Department of Computer Science and Engineering, University of Minnesota, Minneapolis, MN 55455, USA. E-mail: {cheng,dzd,jkim,hngo}@cs.umn.edu.