Optimal algorithms for two-dimensional box placement problems

Authors:
Wenbin Zhu;Wee-Chong Oon;Yujian Weng;Andrew Lim
Affiliations:
Department of Computer Science, Hong Kong Univ. of Science and Technology, Kowloon, Hong Kong;Department of Management Sciences, City University of Hong Kong, Kowloon Tong, Hong Kong;Global R&D Center, Beijing Yahoo!, Tsinghua Science Park, Beijing, P.R. China;Department of Management Sciences, City University of Hong Kong, Kowloon Tong, Hong Kong
Venue:
IEA/AIE'11 Proceedings of the 24th international conference on Industrial engineering and other applications of applied intelligent systems conference on Modern approaches in applied intelligence - Volume Part II
Year:
2011

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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.