On Preemptive Resource Constrained Scheduling: Polynomial-Time Approximation Schemes
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Scheduling Malleable Parallel Tasks: An Asymptotic Fully Polynomial-Time Approximation Scheme
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Approximation Algorithms for Fractional Covering and Packing Problems, and Applications
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
On strip packing With rotations
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Faster and simpler approximation algorithms for mixed packing and covering problems
Theoretical Computer Science
Scientific contributions of Leo Khachiyan (a short overview)
Discrete Applied Mathematics
Parameterized approximation scheme for the multiple knapsack problem
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A Structural Lemma in 2-Dimensional Packing, and Its Implications on Approximability
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
SIAM Journal on Computing
Parameterized Approximation Scheme for the Multiple Knapsack Problem
SIAM Journal on Computing
Scheduling jobs on heterogeneous platforms
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Implementation of approximation algorithms for the max-min resource sharing problem
WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
On efficient weighted rectangle packing with large resources
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Approximation algorithms for mixed fractional packing and covering problems
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
Approximation algorithms for min-max and max-min resource sharing problems, and applications
Efficient Approximation and Online Algorithms
A(3/2+ε) approximation algorithm for scheduling moldable and non-moldable parallel tasks
Proceedings of the twenty-fourth annual ACM symposium on Parallelism in algorithms and architectures
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
An approximation algorithm for the general mixed packing and covering problem
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
IPCO'13 Proceedings of the 16th international conference on Integer Programming and 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
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We present a Lagrangian decomposition algorithm which uses logarithmic potential reduction to compute an $\varepsilon$-approximate solution of the general max-min resource sharing problem with M nonnegative concave constraints on a convex set B. We show that this algorithm runs in $O(M(\varepsilon^{-2}+{\rm ln} M))$ iterations, a data independent bound which is optimal up to polylogarithmic factors for any fixed relative accuracy $\varepsilon\in(0,1)$. In the block-angular case, B is the product of K convex sets (blocks) and each constraint function is block separable. For such models, an iteration of our method requires a $\Theta(\varepsilon)$-approximate solution of K independent block maximization problems which can be computed in parallel.