Journal of Parallel and Distributed Computing
Developments from a June 1996 seminar on Online algorithms: the state of the art
Developments from a June 1996 seminar on Online algorithms: the state of the art
Removable Online Knapsack Problems
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
On rectangle packing: maximizing benefits
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal online bounded space multidimensional packing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Online Scheduling with Bounded Migration
Mathematics of Operations Research
An on-line algorithm for the rectangle packing problem with rejection
WEA'03 Proceedings of the 2nd international conference on Experimental and efficient algorithms
On the two-dimensional Knapsack Problem
Operations Research Letters
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The online removable square packing problem is a two dimensional version of the online removable Knapsack problem. For a sequence of squares with side length at most 1, we are requested to pack a subset of them into a unit square in an online fashion where the online player can decide whether to take the current square or not and which squares currently in the unit square to remove. The goal is to maximize the total packed area. Our results include: (i) Any online algorithm cannot achieve a better competitive ratio than ($\sqrt{5}+3)/2 \approx 2.618$. (ii) The matching upper bound is achieved by a relatively simple online algorithm if repacking is allowed. (iii) Without repacking, we can achieve an upper bound of 3 by using the concept of bricks by Januszewski and Lassak [11]. (iv) The offline version of the problem admits a PTAS.