Optimal rectangle packing

Richard Korf (), Michael Moffitt () and Martha Pollack ()

Annals of Operations Research, 2010, vol. 179, issue 1, 295 pages

Abstract: 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 constraint-satisfaction 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 approaches dramatically outperform previous approaches to optimal rectangle packing. For problems where the rectangle dimensions have low precision, such as small integers, absolute placement is generally more efficient, whereas for rectangles with high-precision dimensions, relative placement will be more effective. In two sets of experiments, we find both the smallest rectangles and squares that can contain the set of squares of size 1×1, 2×2,…,N×N, for N up to 27. In addition, we solve an open problem dating to 1966, concerning packing the set of consecutive squares up to 24×24 in a square of size 70×70. Finally, we find the smallest enclosing rectangles that can contain a set of unoriented rectangles of size 1×2, 2×3, 3×4,…,N×(N+1), for N up to 25. Copyright Springer Science+Business Media, LLC 2010

Keywords: Rectangle packing; Constraint satisfaction; Search (search for similar items in EconPapers)
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10479-008-0463-6 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:annopr:v:179:y:2010:i:1:p:261-295:10.1007/s10479-008-0463-6

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1007/s10479-008-0463-6

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().