Scheduling independent tasks on uniform processors
SIAM Journal on Computing
Tighter bounds for LPT scheduling on uniform processors
SIAM Journal on Computing
A Strip-Packing Algorithm with Absolute Performance Bound 2
SIAM Journal on Computing
Reverse-Fit: A 2-Optimal Algorithm for Packing Rectangles
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Scheduling parallel jobs to minimize the makespan
Journal of Scheduling
Performance Guarantees of Local Search for Multiprocessor Scheduling
INFORMS Journal on Computing
Algorithmic Game Theory
On-line scheduling of parallel jobs in a list
Journal of Scheduling
(Almost) optimal coordination mechanisms for unrelated machine scheduling
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Efficient coordination mechanisms for unrelated machine scheduling
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Coordination mechanisms for selfish scheduling
Theoretical Computer Science
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
A fast 5/2-approximation algorithm for hierarchical scheduling
EuroPar'10 Proceedings of the 16th international Euro-Par conference on Parallel processing: Part I
Theoretical Computer Science
A (5/3 + ε)-approximation for strip packing
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Approximation algorithms for multiple strip packing
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
New approximability results for 2-dimensional packing problems
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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A set of parallel jobs must be scheduled in a grid, which has multi clusters that consist of many identical processors, to minimize the global objective function, the makespan. A parallel job requires several processors for simultaneously executing and it needs some unit times to finish its execution. In practice, each parallel job is owned by an independent agent, which is selfish and select a cluster to minimize its own completion time. This scenario can be represented as a coordination mechanism game, in which the players are job owners, and the strategies are the clusters, and the player's disutility is the completion time of its job in the corresponding schedule. In this work, we design and analyze coordination mechanisms for machines, which aim to minimize the price of anarchy. We study two classes of scheduling policies, the Bottom-Left based algorithms and the Shelf-Packing based algorithms, both in a homogeneous grid and in a heterogeneous grid. We derive upper and lower bounds on the price of anarchy of these coordination mechanisms. We also show that such games are potential games that converge in a linear number of rounds.