Issue |
RAIRO-Theor. Inf. Appl.
Volume 47, Number 4, October-December 2013
|
|
---|---|---|
Page(s) | 315 - 324 | |
DOI | https://doi.org/10.1051/ita/2013037 | |
Published online | 23 August 2013 |
A note on a two dimensional knapsack problem with unloading constraints∗
Institute of Computing, University of Campinas - UNICAMP,
Av. Albert Einstein,
1251, Campinas, Brazil.
jmoises@ic.unicamp.br; ecx@ic.unicamp.br;
fkm@ic.unicamp.br
Received:
22
November
2012
Accepted:
30
May
2013
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.
Mathematics Subject Classification: 68W25 / 05B40 / 90C27
Key words: Knapsack problem / approximation algorithms / unloading/loading constraints
© EDP Sciences 2013
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