no. 4
A note on a two dimensional knapsack problem with unloading constraints
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 47 (2013) no. 4, pp. 315-324.

In this paper we address the two-dimensional knapsack problem with unloading constraints: we have a bin B, and a list L of n rectangular items, each item with a class value in {1,...,C}. The problem is to pack a subset of L into B, maximizing the total profit of packed items, where the packing must satisfy the unloading constraint: while removing one item a, items with higher class values can not block a. We present a (4 + ϵ)-approximation algorithm when the bin is a square. We also present (3 + ϵ)-approximation algorithms for two special cases of this problem.

DOI : 10.1051/ita/2013037
Classification : 68W25, 05B40, 90C27
Mots clés : knapsack problem, approximation algorithms, unloading/loading constraints 
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Moisés da Silveira, Jefferson Luiz; Xavier, Eduardo Candido; Miyazawa, Flávio Keidi. A note on a two dimensional knapsack problem with unloading constraints. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 47 (2013) no. 4, pp. 315-324. doi : 10.1051/ita/2013037. http://www.numdam.org/articles/10.1051/ita/2013037/

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