Optimal Algorithms for Two-Dimensional Box Placement Problems
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.
Keywordsrectangle placement box placement cutting and packing VLSI layout combinatorial optimization
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