Scheduling to minimize power consumption using submodular functions

Demaine, Erik D.; Zadimoghaddam, Morteza

doi:10.1145/1810479.1810483

Cited by 6 publications

(4 citation statements)

References 11 publications

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“…Demaine et al [9] gave an exact algorithm for the multiprocessor gap minimization problem with unit-size tasks. Several further generalizations -for example the set-cover-hard case when each job has several disjoint release time-deadline intervals to choose from -of the problem were considered in [9,10].…”

Section: Further Related Workmentioning

confidence: 99%

Parallel Machine Scheduling to Minimize Energy Consumption

Antoniadis¹,

Garg²,

Kumar³

et al. 2020

Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms

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Given n jobs with release dates, deadlines and processing times we consider the problem of scheduling them on m parallel machines so as to minimize the total energy consumed. Machines can enter a sleep state and they consume no energy in this state. Each machine requires Q units of energy to awaken from the sleep state and in its active state the machine can process jobs and consumes a unit of energy per unit time. We allow for preemption and migration of jobs and provide the first constant approximation algorithm for this problem.

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Section: Further Related Workmentioning

confidence: 99%

Parallel Machine Scheduling to Minimize Energy Consumption

Antoniadis¹,

Garg²,

Kumar³

et al. 2020

Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms

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“…Demaine and Zadimoghaddam [19] recently studied the problem of minimizing energy consumption in schedules over multiple processors. Their model is quite general in that the feasible time slots in which each unit length job may be scheduled may not comprise a single time interval.…”

Section: Related Workmentioning

confidence: 99%

A Model for Minimizing Active Processor Time

2013

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We introduce the following elementary scheduling problem. We are given a collection of n jobs, where each job J i has an integer length ℓ i as well as a set T i 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 so long as it is "active" at t. The goal is to schedule all the jobs in the fewest number 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 non-zero). In other words, subject to ℓ i 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 T i is a single interval. For general T i , we show that the problem is N P -complete 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 triangle-free 2-matching on a special graph. We extend the algorithm of Babenko et. al.[5] to handle our variant, and also to handle non-unit length jobs. This yields an O( √ Lm) time algorithm to solve the preemptive scheduling problem for B = 2, where L = i ℓ i . We also show that for B = 2 and unit length jobs, the optimal non-preemptive schedule has ≤ 4/3 times the active time of the optimal preemptive schedule; this bound extends to several versions of the problem when jobs have arbitrary length.

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“…Demaine and Zadimoghaddam [9] recently considered a different scheduling problem of minimizing cumulative energy consumption for unit-length jobs over multiple processors, demonstrating that the coverage function is submodular, i.e. that the greedy algorithm yields an O(log n)-approximation.…”

Section: Covering Problemsmentioning

confidence: 99%

A Min-Edge Cost Flow Framework for Capacitated Covering Problems

Chang¹,

Khuller²

2013

2013 Proceedings of the Fifteenth Workshop on Algorithm Engineering and Experiments (ALENEX)

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In this work, we introduce the Cov-MECF framework, a special case of minimum-edge cost flow in which the input graph is bipartite. We observe that several important covering (and multi-covering) problems are captured in this unifying model and introduce a new heuristic LP O for any problem in this framework. The essence of LP O harnesses as an oracle the fractional solution in deciding how to greedily modify the partial solution. We empirically establish that this heuristic returns solutions that are higher in quality than those of Wolsey's algorithm. We also apply the analogs of Leskovec et. al. 's [25] optimization to LP O and introduce a further freezing optimization to both algorithms. We observe that the former optimization generally benefits LP O more than Wolsey's algorithm, and that the additional freezing step often corrects suboptimalities while further reducing the number of subroutine calls. We tested these implementations on randomly generated testbeds, several instances from the Second DIMACS Implementation Challenge and a couple networks modeling realworld dynamics.

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Scheduling to minimize power consumption using submodular functions

Cited by 6 publications

References 11 publications

Parallel Machine Scheduling to Minimize Energy Consumption

Parallel Machine Scheduling to Minimize Energy Consumption

A Model for Minimizing Active Processor Time

A Min-Edge Cost Flow Framework for Capacitated Covering Problems

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