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Search Strategies for Rectangle Packing

  • Helmut Simonis
  • Barry O’Sullivan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5202)

Abstract

Rectangle (square) packing problems involve packing all squares with sizes 1 ×1 to n ×n into the minimum area enclosing rectangle (respectively, square). Rectangle packing is a variant of an important problem in a variety of real-world settings. For example, in electronic design automation, the packing of blocks into a circuit layout is essentially a rectangle packing problem. Rectangle packing problems are also motivated by applications in scheduling. In this paper we demonstrate that an “off-the-shelf” constraint programming system, SICStus Prolog, outperforms recently developed ad-hoc approaches by over three orders of magnitude. We adopt the standard CP model for these problems, and study a variety of search strategies and improvements to solve large rectangle packing problems. As well as being over three orders of magnitude faster than the current state-of-the-art, we close eight open problems: two rectangle packing problems and six square packing problems. Our approach has other advantages over the state-of-the-art, such as being trivially modifiable to exploit multi-core computing platforms to parallelise search, although we use only a single-core in our experiments. We argue that rectangle packing is a domain where constraint programming significantly outperforms hand-crafted ad-hoc systems developed for this problem. This provides the CP community with a convincing success story.

Keywords

Constraint Programming Packing Problem Placement Problem Interval Size Interval Strategy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Helmut Simonis
    • 1
  • Barry O’Sullivan
    • 1
  1. 1.Cork Constraint Computation Centre Department of Computer ScienceUniversity College CorkIreland

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