Harmonic algorithm for 3-dimensional strip packing problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Packing Rectangles into 2OPT Bins Using Rotations
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Two for One: Tight Approximation of 2D Bin Packing
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Improved Absolute Approximation Ratios for Two-Dimensional Packing Problems
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Approximation algorithms for orthogonal packing problems for hypercubes
Theoretical Computer Science
A Structural Lemma in 2-Dimensional Packing, and Its Implications on Approximability
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
1-Bounded Space Algorithms for 2-Dimensional Bin Packing
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Bin-packing multi-depots vehicle scheduling problem and its ant colony optimization
CCDC'09 Proceedings of the 21st annual international conference on Chinese control and decision conference
Resource allocation algorithms for virtualized service hosting platforms
Journal of Parallel and Distributed Computing
Dynamic multi-dimensional bin packing
Journal of Discrete Algorithms
Online algorithm for 1-space bounded multi-dimensional bin packing
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Service deactivation aware placement and defragmentation in enterprise clouds
Proceedings of the 7th International Conference on Network and Services Management
Vector bin packing with multiple-choice
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Absolute approximation ratios for packing rectangles into bins
Journal of Scheduling
Competitive multi-dimensional dynamic bin packing via l-shape bin packing
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
Vector bin packing with multiple-choice
Discrete Applied Mathematics
Rectangle packing with one-dimensional resource augmentation
Discrete Optimization
Non-cooperative games on multidimensional resource allocation
Future Generation Computer Systems
Online algorithms for 1-space bounded multi dimensional bin packing and hypercube packing
Journal of Combinatorial Optimization
On the weak computability of a four dimensional orthogonal packing and time scheduling problem
Theoretical Computer Science
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In this paper we introduce a new general framework for set covering problems, based on the combination of randomized rounding of the (near-)optimal solution of the Linear Programming (LP) relaxation, leading to a partial integer solution, and the application of a well-behaved approximation algorithm to complete this solution. If the value of the solution returned by the latter can be bounded in a suitable way, as is the case for the most relevant generalizations of bin packing, the method leads to improved approximation guarantees, along with a proof of tighter integrality gaps for the LP relaxation. Applying our general framework we obtain a polynomial-time randomized algorithm for d-dimensional vector packing with approximation guarantee arbitrarily close to ln d + 1. For d = 2, this value is 1.693 . . ., i.e., we break the natural 2 "barrier" for this case. Moreover, for small values of d this is a notable improvement over the previously-known O(ln d) guarantee by Chekuri and Khanna [5]. For 2-dimensional bin packing with and without rotations, we construct algorithms with performance guarantee arbitrarily close to 1.525 . . ., improving upon previous algorithms with performance guarantee of 2 + \varepsilon by Jansen and Zhang [12] for the problem with rotations and 1.691 . . . by Caprara [2] for the problem without rotations. The previously-unknown key property used in our proofs follows from a retrospective analysis of the implications of the landmark bin packing approximation scheme by Fernandez de la Vega and Lueker [7]. We prove that their approximation scheme is "subset oblivious", which leads to numerous applications. Another byproduct of our paper is an algorithm that solves a well-known configuration LP for 2-dimensional bin packing within a factor of (1 + \varepsilon) for any \varepsilon \ge 0. Interestingly, we do it without using an approximate separation oracle, which would correspond to a well-known geometric 2- dimensional knapsack. Although separation and optimization are equivalent [10] and the existence of an approximation scheme for the separation problem remains open, we are able to design an approximation scheme for the configuration LP since its objective function is unweighed.