Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
An approximation algorithm for the generalized assignment problem
Mathematical Programming: Series A and B
Scheduling to minimize average completion time: off-line and on-line approximation algorithms
Mathematics of Operations Research
Exact and Approximate Algorithms for Scheduling Nonidentical Processors
Journal of the ACM (JACM)
Convex quadratic and semidefinite programming relaxations in scheduling
Journal of the ACM (JACM)
All-Norm Approximation Algorithms
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Improved Scheduling Algorithms for Minsum Criteria
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
Approximation Schemes for Scheduling on Uniformly Related and Identical Parallel Machines
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
Load balancing in the L/sub p/ norm
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Approximation Algorithms for Scheduling on Multiple Machines
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Taxes for linear atomic congestion games
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Graph balancing: a special case of scheduling unrelated parallel machines
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Better bounds for online load balancing on unrelated machines
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
An Optimal On-Line Algorithm for Preemptive Scheduling on Two Uniform Machines in the lpNorm
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
A Lower Bound for the On-Line Preemptive Machine Scheduling with lpNorm
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
A unified approach to scheduling on unrelated parallel machines
Journal of the ACM (JACM)
Improved lower bounds for non-utilitarian truthfulness
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
Taxes for linear atomic congestion games
ACM Transactions on Algorithms (TALG)
Energy efficient scheduling via partial shutdown
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Return of the boss problem: competing online against a non-adaptive adversary
FUN'10 Proceedings of the 5th international conference on Fun with algorithms
Approximate optimization for proportional fair AP association in multi-rate WLANs
WASA'10 Proceedings of the 5th international conference on Wireless algorithms, systems, and applications
Computers and Operations Research
Improved lower bounds for non-utilitarian truthfulness
Theoretical Computer Science
Concentration inequalities for nonlinear matroid intersection
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Tight bounds for selfish and greedy load balancing
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Journal of Scheduling
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ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
AP Association for Proportional Fairness in Multirate WLANs
IEEE/ACM Transactions on Networking (TON)
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We consider the classical problem of scheduling parallel unrelated machines. Each job is to be processed by exactly one machine. Processing job j on machine i requires time pij. The goal is to find a schedule that minimizes the lp norm. Previous work showed a 2-approximation algorithm for the problem with respect to the l∞ norm. For any fixed lp norm the previously known approximation algorithm has a performance of θ(p). We provide a 2-approximation algorithm for any fixed lp norm (p1). This algorithm uses convex programming relaxation. We also give a √ 2-approximation algorithm for the l2 norm. This algorithm relies on convex quadratic programming relaxation. To the best of our knowledge, this is the first time that general convex programming techniques (apart from SDPs and CQPs) are used in the area of scheduling. We show for any given lp norm a PTAS for any fixed number of machines. We also consider the multidimensional generalization of the problem in which the jobs are d-dimensional. Here the goal is to minimize the lp norm of the generalized load vector, which is a matrix where the rows represent the machines and the columns represent the jobs dimension. For this problem we give a (d+1)-approximation algorithm for any fixed lp norm (p1).