We characterize separable multidimensional permutations in terms of forbidden patterns and enumerate them by means of generating function, recursive formula, and explicit formula. We find a connection between multidimensional permutations and guillotine partitions of a box. In particular, a bijection between separable d-dimensional permutations and guillotine partitions of a 2d−1-dimensional bo...

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.

We consider a Two-Dimensional Cutting Stock Problem where stock of different sizes is available, and a set of rectangular items has to be obtained through two-staged guillotine cuts. We propose a heuristic algorithm, based on column generation, which requires as subproblem the solution of a Two-Dimensional Knapsack Problem with two-staged guillotines cuts. A further contribution of the paper co...

A soft solid is more easily sliced using a combination of normal and shearing deformations rather than diced by squeezing down on it normally with the same knife. To explain why this is so, we experimentally probe the slicing and dicing of a soft agar gel with a wire, and complement this with theory and numerical simulations of cutting of a highly deformable solid. We find that purely normal de...

We consider two-dimensional rectangular strip packing without rotation of items and without the guillotine cutting constraint. We propose a single-pass heuristic which fills every free space in a onedimensional knapsack fashion, i.e. considering only item widths. It appears especially important to assign suitable heuristic “pseudo-values” as profits in this knapsack problem. This simple heurist...

Abstract In this paper, we study the packing optimization problem of square plates under conditions that cutting mode is guillotine cut, number stages cannot exceed 3, and order sequence not considered. Because it difficult to determine constraint in process stacking items into stacks, divide nonlinear integer programming model two establish: one stage stacks followed by splicing them stripes, ...

The standard guillotine-shaped vitreous cutter blade (hereafter named Regular Blade [RB]) did not substantially change over the past 40 years, because of its simple and robust design. The asynchronous suction and cutting action, typical of RB blades, determines complete port obstruction generating flow instability and fluid acceleration that results in limited efficiency and eventually retinal ...

We investigate the two-stage guillotine two-dimensional cutting stock problem. This problem commonly arises in the industry when small rectangular items need to be cut out of large stock sheets. We propose an integer programming formulation that extends the well-known Gilmore and Gomory model by explicitly considering solutions that are obtained by both slitting some stock sheets down their wid...