An approximation scheme for the two-stage, two-dimensional knapsack problem

被引：3
|
作者：
Caprara, Alberto [1 ]
Lodi, Andrea [1 ]
Monaci, Michele [2 ]
机构：
[1] Univ Bologna, DEIS, I-40136 Bologna, Italy
[2] Univ Padua, DEIS, I-35131 Padua, Italy
来源：
DISCRETE OPTIMIZATION | 2010年 / 7卷 / 03期
关键词：
Knapsack problem; Shelf packing; Polynomial time approximation schemes; BIN PACKING; SUM;
D O I：
10.1016/j.disopt.2010.03.003
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
We present an approximation scheme for the two-dimensional version of the knapsack problem which requires packing a maximum-area set of rectangles in a unit square bin, with the further restrictions that packing must be orthogonal without rotations and done in two stages. Achieving a solution which is close to the optimum modulo a small additive constant can be done by taking wide inspiration from an existing asymptotic approximation scheme for two-stage two-dimensional bin packing. On the other hand, getting rid of the additive constant to achieve a canonical approximation scheme appears to be widely nontrivial. (C) 2010 Elsevier B.V. All rights reserved.
引用
收藏
页码：114 / 124
页数：11
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