Theoretical Computer Science - Latin American theoretical informatics
An asymptotic approximation algorithm for 3D-strip packing
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
ACM Transactions on Algorithms (TALG)
Two- and three-dimensional parametric packing
Computers and Operations Research
Three-dimensional packings with rotations
Computers and Operations Research
Hardness of approximation for orthogonal rectangle packing and covering problems
Journal of Discrete Algorithms
Three-dimensional container loading models with cargo stability and load bearing constraints
Computers and Operations Research
Inapproximability results for orthogonal rectangle packing problems with rotations
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
Resource augmentation in two-dimensional packing with orthogonal rotations
Operations Research Letters
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We present approximation algorithms for the orthogonal z-oriented three-dimensional packing problem (TPPz) and analyze their asymptotic performance bound. This problem consists in packing a list of rectangular boxes L=(b1,b2,. . . ,bn) into a rectangular box B=(l,w,\infty)$, orthogonally and oriented in the z-axis, in such a way that the height of the packing is minimized. We say that a packing is oriented in the z-axis when the boxes in L are allowed to be rotated (by ninety degrees) around the z-axis. This problem has some nice applications but has been less investigated than the well-known variant of it---denoted by TPP (three-dimensional orthogonal packing problem)---in which rotations of the boxes are not allowed. The problem TPP can be reduced to TPPz. Given an algorithm for TPPz, we can obtain an algorithm for TPP with the same asymptotic bound. We present an algorithm for TPPz, called R, and three other algorithms, called LS, BS, and SS, for special cases of this problem in which the instances are more restricted. The algorithm LS is for the case in which all boxes in L have square bottoms; BS is for the case in which the box B has a square bottom, and SS is for the case in which the box B and all boxes in L have square bottoms. For an algorithm $\wa$, we denote by $r(\wa)$ the asymptotic performance bound of $\wa$. We show that $2.5\leq r(R)