Optimal Rectangle Packing: An Absolute Placement Approach
نویسندگان
چکیده
منابع مشابه
Optimal Rectangle Packing: An Absolute Placement Approach
We consider the problem of finding all enclosing rectangles of minimum area that can contain a given set of rectangles without overlap. Our rectangle packer chooses the xcoordinates of all the rectangles before any of the y-coordinates. We then transform the problem into a perfect-packing problem with no empty space by adding additional rectangles. To determine the y-coordinates, we branch on t...
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We present a new approach to optimal rectangle packing, an NP-complete problem that can be used to model many simple scheduling tasks. Recent attempts at incorporating artificial intelligence search techniques to the problem of rectangle packing have focused on a CSP formulation, in which partial assignments are defined to be the fixed placement of a subset of rectangles. Our technique takes a ...
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We consider the NP-complete problem of finding an enclosing rectangle of minimum area that will contain a given a set of rectangles. We present two different constraintsatisfaction formulations of this problem. The first searches a space of absolute placements of rectangles in the enclosing rectangle, while the other searches a space of relative placements between pairs of rectangles. Both appr...
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In this paper we consider the problem of placing eeciently a rectangle in a two-dimensional layout that may not have the bottom-left placement property. This problem arises when we apply any one of a number of iterative improvement algorithms to the cutting stock problem or its variants. Chazelle has given an O(n)-time placement algorithm when the layout has the bottom-left property; we extend ...
متن کاملOptimal Rectangle Packing: New Results
We present new results on the problem of finding an enclosing rectangle of minimum area that will contain a given a set of rectangles. Many simple scheduling tasks can be modelled by this NP-complete problem. We present a new lower bound on the amount of wasted space in a partial solution, a new dominance condition that prunes many partial solutions, and extend our algorithms to packing unorien...
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ژورنال
عنوان ژورنال: Journal of Artificial Intelligence Research
سال: 2013
ISSN: 1076-9757
DOI: 10.1613/jair.3735