Stochastic on-line knapsack problems
Mathematical Programming: Series A and B
Average-case analysis of off-line and on-line knapsack problems
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Removable Online Knapsack Problems
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
An Online Partially Fractional Knapsack Problem
ISPAN '05 Proceedings of the 8th International Symposium on Parallel Architectures,Algorithms and Networks
Online Removable Square Packing
Theory of Computing Systems
Optimal Resource Augmentations for Online Knapsack
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Approximation algorithms for orthogonal packing problems for hypercubes
Theoretical Computer Science
A polynomial time approximation scheme for the square packing problem
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Online removable knapsack with limited cuts
Theoretical Computer Science
Packing weighted rectangles into a square
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Online minimization knapsack problem
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
Finite-State online algorithms and their automated competitive analysis
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
On the two-dimensional Knapsack Problem
Operations Research Letters
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In this paper, we study a two-dimensional knapsack problem: packing squares as many as possible into a unit square. Our results are the following: (i)we propose an algorithm called IHS (Increasing Height Shelf), and prove that the packing is optimal if in an optimal packing there are at most 5 squares, and this upper bound is sharp; (ii)if all the squares have side length at most 1k, we propose a simple and fast algorithm with an approximation ratio k^2+3k+2k^2 in time O(nlogn); (iii)we give an EPTAS for the problem, where the previous result in Jansen and Solis-Oba (2008) [16] is a PTAS, not an EPTAS. However our approach does not work on the previous model of Jansen and Solis-Oba (2008) [16], where each square has an arbitrary weight.