Corpus ID: 224427

Optimal Rectangle Packing: Initial Results

@inproceedings{Korf2003OptimalRP,
  title={Optimal Rectangle Packing: Initial Results},
  author={Richard E. Korf},
  booktitle={ICAPS},
  year={2003}
}
  • R. Korf
  • Published in ICAPS 2003
  • Computer Science, Mathematics
Given a set of rectangles with fixed orientations, we want to find an enclosing rectangle of minimum area that contains them all with no overlap. Many simple scheduling tasks can be modelled by this NP-complete problem. We use an anytime branch-and-bound algorithm to solve the problem optimally. Our main contributions are a lower-bound on the amount of wasted space in a partial solution, based on a relaxation of the problem to one-dimensional bin packing, and a dominance condition that allows… Expand
Optimal Rectangle Packing: New Results
  • R. Korf
  • Computer Science, Mathematics
  • ICAPS
  • 2004
TLDR
A new lower bound on the amount of wasted space in a partial solution, a new dominance condition that prunes many partial solutions, and a new algorithms to packing unoriented rectangles on the problem of finding an enclosing rectangle of minimum area that will contain a given a set of rectangles are presented. Expand
Optimal rectangle packing
TLDR
This work considers the NP-complete problem of finding an enclosing rectangle of minimum area that will contain a given a set of rectangles, and presents two different constraint-satisfaction formulations of this problem that dramatically outperform previous approaches to optimal rectangle packing. Expand
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TLDR
These algorithms represent the current state-of-the-art for this problem, outperforming other algorithms by orders of magnitude, depending on the benchmark, and introduce three new benchmarks, avoiding properties that make a benchmark easy, such as rectangles with shared dimensions. Expand
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TLDR
Two new benchmarks are proposed, one where the orientation of the rectangles is fixed and one where it is free, that include rectangles of various aspect ratios that are much more difficult for the previous state-of-the-art solver. Expand
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TLDR
This work transforms the rectangle packing problem into a perfect packing problem that has no empty space, and presents inference rules to reduce the instance size. Expand
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TLDR
This work extends the previously studied square packing problem by adding an additional degree of freedom for each rectangle, deciding in which orientation the item should be packed, and derives a decomposition method that initially only looks at the subproblem given by one of the cumulative constraints. Expand
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TLDR
It is argued that rectangle packing is a domain where constraint programming significantly outperforms hand-crafted ad-hoc systems developed for this problem, and this approach has other advantages over the state-of-the-art, such as being trivially modifiable to exploit multi-core computing platforms to parallelise search. Expand
Optimal Rectangle Packing: A Meta-CSP Approach
TLDR
A new approach to optimal rectangle packing, an NP-complete problem that can be used to model many simple scheduling tasks, is presented, and a suite of new techniques that exploit both the symmetry and geometry present in this particular domain are developed. Expand
Optimal Packing of High-Precision Rectangles
TLDR
This work packs the first 50,000 such rectangles with a greedy heuristic and conjecture that the entire infinite series can fit on the open problem of whether or not one can pack a particular infinite series of rectangles into the unit square. Expand
Bin Packing in Multiple Dimensions: Inapproximability Results and Approximation Schemes
TLDR
It is shown that unlike the one-dimensional case, the two-dimensional packing problem cannot have an asymptotic polynomial time approximation scheme (APTAS), unless PNP, and the first approximation scheme for the problem of placing a collection of rectangles in a minimum-area encasing rectangle is obtained. Expand
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  • R. Korf
  • Computer Science
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The first and the most critical stage in VLSI layout design is the placement, the background of which is the rectangle packing problem: Given many rectangular modules of arbitrary size, place themExpand
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The first and the most critical stage in VLSI layout design is the placement, the background of which is the rectangle packing problem: Given many rectangular modules of arbitrary site, place themExpand
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