Optimal Algorithms for Two-Dimensional Box Placement Problems

  • Wenbin Zhu
  • Wee-Chong Oon
  • Yujian Weng
  • Andrew Lim
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6704)


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.


rectangle placement box placement cutting and packing VLSI layout combinatorial optimization 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Wenbin Zhu
    • 1
  • Wee-Chong Oon
    • 2
  • Yujian Weng
    • 3
  • Andrew Lim
    • 2
  1. 1.Department of Computer ScienceHong Kong Univ. of Science and TechnologyKowloonHong Kong
  2. 2.Department of Management SciencesCity University of Hong KongKowloon TongHong Kong
  3. 3.Global R&D Center, Beijing Yahoo!BeijingP.R. China

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