Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A scheduling model for reduced CPU energy
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Dynamic Speed Scaling to Manage Energy and Temperature
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Algorithmic problems in power management
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Power-aware scheduling for makespan and flow
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Speed scaling to manage energy and temperature
Journal of the ACM (JACM)
Speed scaling on parallel processors
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Energy efficient online deadline scheduling
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Speed scaling for weighted flow time
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
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ACM Transactions on Algorithms (TALG)
Getting the best response for your erg
ACM Transactions on Algorithms (TALG)
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Speed Scaling Functions for Flow Time Scheduling Based on Active Job Count
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
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ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Optimal speed scaling under arbitrary power functions
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Energy efficient deadline scheduling in two processor systems
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
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This paper investigates the problem of scheduling jobs on multiple speed-scaled processors, i.e., we have constant 驴1 such that running a processor at speed s results in energy consumption s 驴 per time unit. We consider the general case where each job has a monotonously increasing cost function that penalizes delay. This includes the so far considered cases of deadlines, flow time, and weighted flow time. For any type of delay cost functions, we obtain the following results: Any β-approximation algorithm for a single processor yields a randomized βB 驴 -approximation algorithm for multiple processors, where B 驴 is the 驴th Bell number, that is, the number of partitions of a set of size 驴. The generated schedule is without migration, but we compare it to an optimal schedule with migration. Hence, this result holds for migratory and non-migratory schedules. Analogously, we show that any β-competitive online algorithm for a single processor yields a βB 驴 -competitive online algorithm for multiple processors. Finally, we show that any β-approximation algorithm for multiple processors with migration yields a deterministic βB 驴 -approximation algorithm for multiple processors without migration. These facts improve several approximation ratios and lead to new results. For instance, we obtain the first constant factor online and offline approximation algorithm for multiple processors without migration for arbitrary release times, deadlines, and job sizes.