New Classes of Lower Bounds for Bin Packing Problems
Proceedings of the 6th International IPCO Conference on Integer Programming and Combinatorial Optimization
An Approximation Scheme for the Two-Stage, Two-Dimensional Bin Packing Problem
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Bin Packing with Item Fragmentation
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
An Asymptotic Fully Polynomial Time Approximation Scheme for Bin Covering
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Polynominal time approximation schemes for class-constrained packing problem
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
Scheduling Malleable Parallel Tasks: An Asymptotic Fully Polynomial-Time Approximation Scheme
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Vector Assignment Problems: A General Framework
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
A Tale of Two Dimensional Bin Packing
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Bin Packing in Multiple Dimensions: Inapproximability Results and Approximation Schemes
Mathematics of Operations Research
Batch scheduling of step deteriorating jobs
Journal of Scheduling
Approximation algorithms for a facility location problem with service capacities
ACM Transactions on Algorithms (TALG)
Bin packing with controllable item sizes
Information and Computation
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
Asymptotic fully polynomial approximation schemes for variants of open-end bin packing
Information Processing Letters
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Multiflows in multihop wireless networks
Proceedings of the tenth ACM international symposium on Mobile ad hoc networking and computing
Hardness of approximation for orthogonal rectangle packing and covering problems
Journal of Discrete Algorithms
Variable-Size Rectangle Covering
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Strip packing with precedence constraints and strip packing with release times
Theoretical Computer Science
Approximation algorithms for orthogonal packing problems for hypercubes
Theoretical Computer Science
Bounded-space online bin cover
Journal of Scheduling
A Structural Lemma in 2-Dimensional Packing, and Its Implications on Approximability
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Bin packing problems with rejection penalties and their dual problems
Information and Computation
On the complexity of variations of equal sum subsets
Nordic Journal of Computing
Approximation schemes for packing splittable items with cardinality constraints
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
Class constrained bin packing revisited
Theoretical Computer Science
Scheduling periodic tasks in a hard real-time environment
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
The train delivery problem: vehicle routing meets bin packing
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
Sharing-aware algorithms for virtual machine colocation
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
Set covering with ordered replacement: additive and multiplicative gaps
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
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
On the configuration-LP for scheduling on unrelated machines
ESA'11 Proceedings of the 19th European conference on Algorithms
A note on the Kenyon-Remila strip-packing algorithm
Information Processing Letters
Mathematics of Operations Research
AFPTAS Results for Common Variants of Bin Packing: A New Method for Handling the Small Items
SIAM Journal on Optimization
Implementation of approximation algorithms for the max-min resource sharing problem
WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
The entropy rounding method in approximation algorithms
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Approximation schemes for packing with item fragmentation
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Bin packing and covering problems with rejection
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Bidimensional packing by bilinear programming
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Approximation algorithms for network design and facility location with service capacities
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Bin packing via discrepancy of permutations
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Improved approximation results for stochastic knapsack problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Inapproximability results for orthogonal rectangle packing problems with rotations
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
A robust APTAS for the classical bin packing problem
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Vector bin packing with multiple-choice
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Bin packing with fixed number of bins revisited
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Fixed-parameter approximation: conceptual framework and approximability results
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Approximation algorithms for min-max and max-min resource sharing problems, and applications
Efficient Approximation and Online Algorithms
Bin packing with rejection revisited
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
An OPT+1 algorithm for the cutting stock problem with constant number of object lengths
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
A fast approximation scheme for the multiple knapsack problem
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
Vector bin packing with multiple-choice
Discrete Applied Mathematics
Two-dimensional bin packing with one-dimensional resource augmentation
Discrete Optimization
Rectangle packing with one-dimensional resource augmentation
Discrete Optimization
A polynomial-time approximation scheme for maximizing the minimum machine completion time
Operations Research Letters
A 3-approximation algorithm for two-dimensional bin packing
Operations Research Letters
An approximation algorithm for square packing
Operations Research Letters
Bin packing as a random walk: A note on knödel's paper
Operations Research Letters
Assigning sporadic tasks to unrelated parallel machines
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
An improved approximation scheme for variable-sized bin packing
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Fast asymptotic FPTAS for packing fragmentable items with costs
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
New approximability results for 2-dimensional packing problems
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
A fast asymptotic approximation scheme for bin packing with rejection
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
Bin packing with fixed number of bins revisited
Journal of Computer and System Sciences
Bin Packing via Discrepancy of Permutations
ACM Transactions on Algorithms (TALG) - Special Issue on SODA'11
Bin covering with cardinality constraints
Discrete Applied Mathematics
A note on a selfish bin packing problem
Journal of Global Optimization
Proceedings of the 22nd ACM international conference on Conference on information & knowledge management
Online algorithms for 1-space bounded multi dimensional bin packing and hypercube packing
Journal of Combinatorial Optimization
A robust AFPTAS for online bin packing with polynomial migration,
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
On the weak computability of a four dimensional orthogonal packing and time scheduling problem
Theoretical Computer Science
Smart-Grid electricity allocation via strip packing with slicing
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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We present several polynomial-time approximation algorithms for the one-dimensional bin-packing problem. using a subroutine to solve a certain linear programming relaxation of the problem. Our main results are as follows: There is a polynomial-time algorithm A such that A(I) ≤ OPT(I) + O(log2 OPT(I)). There is a polynomial-time algorithm A such that, if m(I) denotes the number of distinct sizes of pieces occurring in instance I, then A(I) ≤ OPT(I) + O(log2 m(I)). There is an approximation scheme which accepts as input an instance I and a positive real number ε, and produces as output a packing using as most (1 + ε) OPT(I) + O(ε-2) bins. Its execution time is O(ε-c n log n), where c is a constant. These are the best asymptotic performance bounds that have been achieved to date for polynomial-time bin-packing. Each of our algorithms makes at most O(log n) calls on the LP relaxation subroutine and takes at most O(n log n) time for other operations. The LP relaxation of bin packing was solved efficiently in practice by Gilmore and Gomory. We prove its membership in P, despite the fact that it has an astronomically large number of variables.