Abstract
The two-dimensional box placement problem involves finding a position to place a rectangular box into a container given n rectangular boxes that have already been placed. It commonly arises as a subproblem in many algorithms for cutting stock and packing problems. We develop an asymptotically optimal approach for finding the bottom-leftmost feasible position, and modify it to find all normal feasible positions (which is also asymptotically optimal). Our approach relies on augmented versions of the segment tree data structure, and is simpler and more practicable than the best existing approach. Furthermore, it does not require that the placed boxes are interior-disjoint.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Berg, M., Cheong, O., Kreveld, M., Overmars, M.: Computational Geometry: Algorithms and Applications, 3rd edn. Springer, Heidelberg (2008), http://www.worldcat.org/isbn/3540779736
de Berg, M., Cheong, O., van Kreveld, M., Overmars, M.: Segment Trees, 3rd edn., ch. 10.3. Springer, Heidelberg (2008)
Healy, P., Creavin, M., Kuusik, A.: An optimal algorithm for rectangle placement. Operations Research Letters 24(1-2) (February 1999), http://www.sciencedirect.com/science/article/B6V8M-43GHSPF-B/2/42b6ea739a362592dccfb090350a5a34
Wood, D.: The contour problem for rectilinear polygons. Information Processing Letters 19(5), 229–236 (1984) http://dx.doi.org/10.1016/0020-0190(84)90058-9
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhu, W., Oon, WC., Weng, Y., Lim, A. (2011). Optimal Algorithms for Two-Dimensional Box Placement Problems. In: Mehrotra, K.G., Mohan, C.K., Oh, J.C., Varshney, P.K., Ali, M. (eds) Modern Approaches in Applied Intelligence. IEA/AIE 2011. Lecture Notes in Computer Science(), vol 6704. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21827-9_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-21827-9_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21826-2
Online ISBN: 978-3-642-21827-9
eBook Packages: Computer ScienceComputer Science (R0)