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15
Race to Idle: New Algorithms for Speed Scaling with a Sleep State
"... We study an energy conservation problem where a variablespeed processor is equipped with a sleep state. Executing jobs at high speeds and then setting the processor asleep is an approach that can lead to further energy savings compared to standard dynamic speed scaling. We consider classical deadlin ..."
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We study an energy conservation problem where a variablespeed processor is equipped with a sleep state. Executing jobs at high speeds and then setting the processor asleep is an approach that can lead to further energy savings compared to standard dynamic speed scaling. We consider classical deadlinebased scheduling, i.e. each job is specified by a release time, a deadline and a processing volume. For general convex power functions, Irani et al. [12] devised an offline 2approximation algorithm. Roughly speaking, the algorithm schedules jobs at a critical speed scrit that yields the smallest energy consumption while jobs are processed. For power functions P(s) = s α +γ, where s is the processor speed, Han et al. [11] gave an (α α + 2)competitive online algorithm. We investigate the offline setting of speed scaling with a sleep state. First we prove NPhardness of the optimization problem. Additionally, we develop lower bounds, for general convex power functions: No algorithm that constructs scritschedules, which execute jobs at speeds of at least scrit, can achieve an approximation factor smaller than 2. Furthermore, no algorithm that minimizes the energy expended for processing jobs can attain an approximation ratio smaller than 2. We then present an algorithmic framework for designing good approximation algorithms. For general convex power functions, we derive an approximation factor of 4/3. For powerfunctionsP(s) = βs α +γ, weobtainanapproximation of 137/117 < 1.171. We finally show that our framework yields the best approximation guarantees for the class of scritschedules. For general convex power functions, we give another 2approximation algorithm. For functions P(s) = βs α + γ, we present tight upper and lower bounds on the best possible approximation factor. The ratio is exactly eW−1(−e −1−1/e)/(eW−1(−e −1−1/e) + 1) < 1.211, where W−1 is the lower branch of the Lambert W function. 1
Algorithms for dynamic speed scaling
 In STACS 2011, volume 9 of LIPIcs. Schloss Dagstuhl  LeibnizZentrum fuer Informatik
, 2011
"... Many modern microprocessors allow the speed/frequency to be set dynamically. The general goal is to execute a sequence of jobs on a variablespeed processor so as to minimize energy consumption. This paper surveys algorithmic results on dynamic speed scaling. We address settings where (1) jobs have ..."
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Cited by 13 (0 self)
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Many modern microprocessors allow the speed/frequency to be set dynamically. The general goal is to execute a sequence of jobs on a variablespeed processor so as to minimize energy consumption. This paper surveys algorithmic results on dynamic speed scaling. We address settings where (1) jobs have strict deadlines and (2) job flow times are to be minimized.
Algorithms for Energy Saving
, 2010
"... Energy has become a scarce and expensive resource. There is a growing awareness in society that energy saving is a critical issue. This paper surveys algorithmic solutions to reduce energy consumption in computing environments. We focus on the system and device level. More specifically, we study po ..."
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Cited by 5 (0 self)
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Energy has become a scarce and expensive resource. There is a growing awareness in society that energy saving is a critical issue. This paper surveys algorithmic solutions to reduce energy consumption in computing environments. We focus on the system and device level. More specifically, we study powerdown mechanisms as well as dynamic speed scaling techniques in modern microprocessors.
A Model for Minimizing Active Processor Time
"... We introduce the following elementary scheduling problem. We are given a collection of n jobs, where each job Ji has an integer length ℓi as well as a set Ti of time intervals in which it can be feasibly scheduled. Given a parameter B, the processor can schedule up to B jobs at a timeslot t solongas ..."
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Cited by 5 (3 self)
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We introduce the following elementary scheduling problem. We are given a collection of n jobs, where each job Ji has an integer length ℓi as well as a set Ti of time intervals in which it can be feasibly scheduled. Given a parameter B, the processor can schedule up to B jobs at a timeslot t solongasit is “active”att. The goalis toschedule allthe jobs in the fewestnumber of active timeslots. The machine consumes a fixed amount of energy per active timeslot, regardless of the number of jobs scheduled in that slot (as long as the number of jobs is nonzero). In other words, subject to ℓi units of each job i being scheduled in its feasible region and at each slot at most B jobs being scheduled, we are interested in minimizing the total time during which the machine is active. We present a linear time algorithm for the case where jobs are unit length and each Ti is a single interval. For general Ti, we show that the problem is NPcomplete even for B = 3. However when B = 2, we show that it can be efficiently solved. In addition, we consider a version of the problem where jobs have arbitrary lengths and can be preempted at any point in time. For general B, the problem can be solved by linear programming. For B = 2, the problem amounts to finding a trianglefree 2matching on a special graph. We extend the algorithm of Babenko et. al. [5] to handle our variant, and also to handle nonunit length jobs. This yields an O ( √ Lm) time algorithm to solve the preemptive scheduling problem for B = 2, where L = ∑ iℓi. We alsoshow that for B = 2 and unit length jobs, the optimal nonpreemptive schedule has ≤ 4/3times the activetime of the optimal preemptive schedule; this bound extends to several versions of the problem when jobs have arbitrary length. 1
Slow Down & Sleep for Profit in Online Deadline Scheduling
, 2012
"... We present and study a new model for energyaware and profitoriented scheduling on a single processor. The processor features dynamic speed scaling as well as suspension to a sleep mode. Jobs arrive over time, are preemptable, and have different sizes, values, and deadlines. On the arrival of a n ..."
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Cited by 2 (2 self)
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We present and study a new model for energyaware and profitoriented scheduling on a single processor. The processor features dynamic speed scaling as well as suspension to a sleep mode. Jobs arrive over time, are preemptable, and have different sizes, values, and deadlines. On the arrival of a new job, the scheduler may either accept or reject the job. Accepted jobs need a certain energy investment to be finished in time, while rejected jobs cause costs equal to their values. Here, power consumption at speed s is given by P (s) = sα + β and the energy investment is power integrated over time. Additionally, the scheduler may decide to suspend the processor to a sleep mode in which no energy is consumed, though awaking entails fixed transition costs γ. The objective is to minimize the total value of rejected jobs plus the total energy. Our model combines aspects from advanced energy conservation techniques (namely speed scaling and sleep states) and profitoriented scheduling models. We show that rejectionoblivious schedulers (whose rejection decisions are not based on former decisions) have – in contrast to the model without sleep states – an unbounded competitive ratio w.r.t. the processor parameters α and β. It turns out that the worstcase performance of such schedulers depends linearly on the jobs ’ value densities (the ratio between a job’s value and its work). We give an algorithm whose competitiveness nearly matches this lower bound. If the maximum value density is not too large, the competitiveness becomes αα + 2eα. Also, we show that it suffices to restrict the value density of lowvalue jobs only. Using a technique from [12] we transfer our results to processors with a fixed maximum speed.
EnergyEfficient Algorithms  Algorithmic solutions can help reduce energy consumption in computing environs
, 2010
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Online PowerManaging Strategy with Hard RealTime Guarantees
, 2014
"... We consider the problem of online dynamic power management that provides hard realtime guarantees. In this problem, each of the given jobs is associated with an arrival time, a deadline, and an execution time, and the objective is to decide a schedule of the jobs as well as a sequence of state tran ..."
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We consider the problem of online dynamic power management that provides hard realtime guarantees. In this problem, each of the given jobs is associated with an arrival time, a deadline, and an execution time, and the objective is to decide a schedule of the jobs as well as a sequence of state transitions on the processors so as to minimize the total energy consumption. In this paper, we examine the problem complexity and provide online strategies to achieve energyefficiency. First, we show that the competitive factor of any online algorithm for this problem is at least 2.06. Then we present an online algorithm which gives a 4competitive schedule. When the execution times of the jobs are unit, we show that the competitive factor improves to 3.59. At the end, the algorithm is generalized to allow a tradeoff between the number of processors we use and the energyefficiency of the resulting schedule.
Minimal Routing Cooperation using Route Weight for MANET
"... Now days people moves to flexible and wireless network facilities hence Mobile adhoc network and sensor networks are growing very fast. Adhoc network can performed great task using multihop communication in such environment where dedicated infrastructure is hard to established, where node are mov ..."
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Now days people moves to flexible and wireless network facilities hence Mobile adhoc network and sensor networks are growing very fast. Adhoc network can performed great task using multihop communication in such environment where dedicated infrastructure is hard to established, where node are movable and topology changes rapidly. Such type of network have to suffer with several constraints for example limited energy of nodes, information of the coordinate location of the mobile nodes at any geographical location, and need of realtime or multicast communication. Lots of research has been done in this field as importance and challenges in this field for covering various situations. This paper gives detail classification of the ad hoc routing protocols and to survey and proposed a new method for effective route discovery. Proposed scheme is based on total delay of path and remain power of path for selection route between source and destination. Proposed method is expected to be more effective and efficient route discovery from existing. Keywords Ad hoc networks, sensor networks, routing protocols,
Extra Buffer Resources Improving Competitiveness in Minimizing Energy Consumption
"... In this paper, we consider energy management algorithms for scheduling jobs in powerscare scenarios such as embedded computer systems and sensor networks. We focus on investigating the impact of buffer resources in minimizing the total energy cost in an online setting. The online algorithms do not ..."
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In this paper, we consider energy management algorithms for scheduling jobs in powerscare scenarios such as embedded computer systems and sensor networks. We focus on investigating the impact of buffer resources in minimizing the total energy cost in an online setting. The online algorithms do not have any assumptions on job arrivals; their worstcase performance is measured in term of competitive ratio, when they are compared with the optimal algorithms with clairvoyance. We prove that with appropriate extra buffer space, an online algorithm can beat an weak optimal offline algorithm in terms of the total energy required. Our research result helps to quantitatively estimate the optimal onchip buffer resources allocated in realtime systems with power constraints. We also present the lower bound of competitive ratio that any deterministic online algorithm cannot achieve. 1