Polynomial-time algorithms for minimum energy scheduling
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Citations
Slow Down & Sleep for Profit in Online Deadline Scheduling
Minimizing Energy on Homogeneous Processors with Shared Memory
A Power-aware Scheduling Algorithm in Multi-tenant IaaS Clouds
Minimizing the Cost of Batch Calibrations
Optimizing energy consumption under flow and stretch constraints
References
Computers and Intractability: A Guide to the Theory of NP-Completeness
Scheduling Algorithms
Algorithmic problems in power management
Related Papers (5)
Frequently Asked Questions (14)
Q2. What is the aim of power management policies?
The aim of power management policies is to reduce the amount of energy consumed by computer systems while maintaining satisfactory level of performance.
Q3. How can the authors show that the algorithm is NP-hard?
The non-preemptive version of their problem, that is 1|rj |E, can be easily shown to be NP-hard in the strong sense, even for L = 1 (when the objective is to only minimize the number of gaps), by reduction from 3-Partition [4, problem SS1].
Q4. How can the authors find the index l in time?
Es to compute, for each s the authors minimize over n values of g, and for fixed s and g the authors can find the index l in time O(log n) with binary search.
Q5. What is the earliest-deadline property of R?
Suppose that there is a time t, u < t ≤ v, such that there are no jobs i ≤ k with u ≤ ri < t, and that R executes some job m < k with rm ≤ u at or after time t.
Q6. What is the way to reduce the time of a l?
(Finding this l can be in fact reduced to amortized time O(1) if the authors process g in increasing order, for then the values of Un,s,g, and thus also of l, increase monotonically as well.)
Q7. What is the way to maximize over pairs?
In the last choice the authors maximize over pairs (l, h) that satisfy the condition rl = Uk−1,s,h + 1, and thus the authors only have O(n) such pairs.
Q8. What is the main difference between the two types of speed scaling policies?
As the energy required to perform the job increases quickly with the speed of the processor, speed scaling policies tend to slow down the processor while ensuring that all jobs meet their deadlines (see [8], for example).
Q9. What is the name of the scheduling problem?
an instance of the scheduling problem 1|rj ; pmtn|E consists of n jobs, where each job j is specified by its processing time pj , release time rj and deadline dj .
Q10. What is the definition of a (k, s)-schedule?
For jobs k and s, a partial schedule S is called a (k, s)-schedule if it schedules all jobs j ≤ k with rs ≤ rj < Cmax(S) (recall that Cmax(S) denotes the completion time of schedule S).
Q11. What is the recurrence relation for Uk,s,g?
For k ≥ 1, Uk,s,g is defined recursively as follows:Uk,s,g ← max l<k,h≤g Uk−1,s,gUk−1,s,g + 1 if rs ≤ rk ≤ Uk−1,s,g & ∀j < k rj 6= Uk−1,s,g dk if g > 0 & ∀j < k rj < Uk−1,s,g−1
Q12. What is the main difference between the two types of jobs?
In these works, however, jobs are critical, that is, they must be executed as soon as they are released, and the online algorithm only needs to determine the appropriate power-down state when the machine is idle.
Q13. What is the way to determine the optimal suspension and wake-up times?
this formula reflects the fact that once the support of a schedule is given, the optimal suspension and wake-up times are easy to determine: the authors suspend the machine during a gap if and only if its length is more than L, for otherwise it would be cheaper to keep the processor on during the gap.
Q14. what is the minimum energy of the whole instance?
El otherwise, where u = Un,s,g, rl = min {rj : rj > u}(5)The minimum energy of the whole instance is then E1, where r1 is the first release time.