### Citations

13827 |
Computers and Intractability. A Guide to the Theory of NP-Completeness
- Garey, Johnson
- 1979
(Show Context)
Citation Context ...HAIN problem is NP-hard, but not known to be in NP. Note that the problem is not known to be in NP because speeds could take any real values (CONTINUOUS model). The completeness comes from SUBSET-SUM =-=[11]-=-. The problem is NP-hard even for a linear chain application mapped on a single processor (and any general DAG mapped on a single processor becomes a linear chain). Proof. Consider the associated deci... |

1888 |
Theory of linear and integer programming
- Schrijver
- 1986
(Show Context)
Citation Context ... min (∑n i=1 ∑m j=1 α(i,j)f 3 j ) . The size of this linear program is clearly polynomial in the size of the instance, all nm variables are rational, and therefore it can be solved in polynomial time =-=[20]-=-. 6 Heuristics for TRI-CRIT-CONT In this section, we propose some polynomial-time heuristics for TRI-CRIT-CONT, which was shown NP-hard (see Theorem 1). We start by outlining the general principles th... |

674 |
Principles of Mathematical Analysis
- Rudin
- 1976
(Show Context)
Citation Context ...direct corollary from the theorem that states that any piecewise-continuous function defined on an interval [a, b] can be uniformly approximated as closely as desired by a piecewise-constant function =-=[20]-=-. Suppose that in the optimal solution, there is a task whose speed changes during the execution. Consider the first time-step at which the change occurs: the computation begins at speed f from time t... |

355 |
Scheduling Algorithms
- Brucker
- 2007
(Show Context)
Citation Context ...eous platform consisting of p identical processors. This problem has been widely studied with the objective of minimizing the total execution time, or makespan, and it is well known to be NP-complete =-=[7]-=-. Since the introduction of DVFS, many papers have dealt with the optimization of energy consumption while enforcing a deadline, i.e., a bound on the makespan [4, 6, 8, 3]. There are many situations i... |

163 | Speed scaling to manage energy and temperature
- Bansal, Kimbrel, et al.
- 2007
(Show Context)
Citation Context ...ironmental reasons. This holds true for traditional computer systems, not even to speak of battery-powered systems. More precisely, a processor running at speed s dissipates s3 watts per unit of time =-=[4, 6, 8]-=-, hence it consumes s3 × d joules when operated during d units of time. To help reduce energy dissipation, processors can run at different speeds. A widely used technique to reduce energy consumption ... |

108 | Run-time voltage hopping for low-power realtime systems
- Lee, Sakurai
(Show Context)
Citation Context ...t is not possible to change the allocation of a task, it is possible to change its speed. This technique, which consists in exploiting the slack due to workload variations, is called slack reclaiming =-=[13, 18]-=-. In our previous work [3], assuming that the mapping and a deadline are given, we have assessed the impact of several speed variation models on the complexity of the problem of minimizing the energy ... |

92 | Energy-aware partitioning for multiprocessor real-time systems - Aydin, Yang - 2003 |

72 | The effects of energy management on reliability in real-time embedded systems
- Zhu, Melhem, et al.
- 2004
(Show Context)
Citation Context ... sum, on each time interval with constant speed f , of the energy consumed during this interval at speed f . While energy consumption can be reduced by using speed scaling techniques, it was shown in =-=[24, 8]-=- that speed scaling increases the number of transient fault rates of the system. In order to make up for the loss in reliability due to the energy efficiency, different models have been proposed for f... |

67 |
Leakage-aware energy-efficient scheduling of real-time tasks in multiprocessor systems
- Chen, Hsu, et al.
- 2006
(Show Context)
Citation Context ...ironmental reasons. This holds true for traditional computer systems, not even to speak of battery-powered systems. More precisely, a processor running at speed s dissipates s3 watts per unit of time =-=[4, 6, 8]-=-, hence it consumes s3 × d joules when operated during d units of time. To help reduce energy dissipation, processors can run at different speeds. A widely used technique to reduce energy consumption ... |

53 | The Interplay of Power Management and Fault Recovery in Real-Time Systems
- MELHEM, MOSSE, et al.
- 2004
(Show Context)
Citation Context ... order to meet the reliability constraints; and (iii) checkpointing consists in "saving" the work done at some certain points of the work, hence reducing the amount of work lost when a failure occurs =-=[14, 23]-=-. This work focuses on the re-execution model, for several reasons. On the one hand, replication is too costly in terms of both resource usage and energy consumption: even if the first execution turns... |

51 | Energy–aware adaptive checkpointing in embedded real time system
- Zhang, Chakraborty
(Show Context)
Citation Context ... order to meet the reliability constraints; and (iii) checkpointing consists in "saving" the work done at some certain points of the work, hence reducing the amount of work lost when a failure occurs =-=[14, 23]-=-. This work focuses on the re-execution model, for several reasons. On the one hand, replication is too costly in terms of both resource usage and energy consumption: even if the first execution turns... |

45 | Fault-aware Job Scheduling for BlueGene/L Systems
- Oliner, Sahoo, et al.
- 2004
(Show Context)
Citation Context ...peed of a processor increases the number of transient fault rates of the system; the probability of failures increases exponentially, and this probability cannot be neglected in large-scale computing =-=[16]-=-. In order to make up for the loss in reliability due to the energy efficiency, different models have been proposed for fault-tolerance: (i) re-execution is the model under study in this work, and it ... |

43 | Scheduling and voltage scaling for energy/reliability trade-offs in fault-tolerant time-triggered embedded systems
- Pop, Poulsen, et al.
- 2007
(Show Context)
Citation Context ...been proposed for fault-tolerance: (i) re-execution is the model under study in this work, and it consists in re-executing a task that does not meet the reliability constraint; it was also studied in =-=[25, 24, 17]-=-; (ii) replication was studied in [1, 12]; this model consists in executing the same task on several processors simultaneously, in order to meet the reliability constraints; and (iii) checkpointing co... |

35 | Fault-Tolerant Platforms for Automotive SafetyCritical Applications
- Baleani, Ferrari, et al.
- 2003
(Show Context)
Citation Context ...ses the fault rate exponentially. The reliability of a task Ti executed once at speed f isRi(f) = e−λ(f)×Exe(wi,f). Because the fault rate is usually very small, of the order of 10−6 per time unit in =-=[5, 17]-=-, 10−5 in [1], we can use the first order approximation of Ri(f) as Ri(f) = 1− λ(f)× Exe(wi, f) = 1− λ̃0 ed̃ fmax−f fmax−fmin × wi f = 1− λ0 e−df × wi f , (2) where d = d̃fmax−fmin and λ0 = λ̃0e dfmax... |

30 | Towards Energy Aware Scheduling for Precedence Constrained Parallel Tasks in a Cluster with DVFS
- Laszewski, Wang
(Show Context)
Citation Context ... are given, we have assessed the impact of several speed variation models on the complexity of the problem of minimizing the energy consumption. Rather than using a local approach such as backfilling =-=[22, 18]-=-, which only reclaims gaps in the schedule, we have considered the problem as a whole. While energy consumption can be reduced by using speed scaling techniques, it was shown in [25, 10] that reducing... |

30 | Energy management for real-time embedded systems with reliability requirements
- Zhu, Aydin
- 2006
(Show Context)
Citation Context ...been proposed for fault-tolerance: (i) re-execution is the model under study in this work, and it consists in re-executing a task that does not meet the reliability constraint; it was also studied in =-=[25, 24, 17]-=-; (ii) replication was studied in [1, 12]; this model consists in executing the same task on several processors simultaneously, in order to meet the reliability constraints; and (iii) checkpointing co... |

24 |
Soft errors issues in low-power caches
- Degalahal, Li, et al.
- 2005
(Show Context)
Citation Context ...s backfilling [22, 18], which only reclaims gaps in the schedule, we have considered the problem as a whole. While energy consumption can be reduced by using speed scaling techniques, it was shown in =-=[25, 10]-=- that reducing the speed of a processor increases the number of transient fault rates of the system; the probability of failures increases exponentially, and this probability cannot be neglected in la... |

24 |
Models and algorithms for reliability-oriented taskallocation in redundant distributed-computer systems
- Shatz, Wang
- 1989
(Show Context)
Citation Context ... task and the processor subject to that failure will be able to recover and execute the subsequent task assigned to it (if any). In addition, we use the reliability model introduced by Shatz and Wang =-=[21]-=-, which states that the radiation-induced transient faults follow a Poisson distribution. The parameter λ of the Poisson distribution is then: λ(f) = λ̃0 e d̃ fmax−ffmax−fmin , (1) where fmin ≤ f ≤ fm... |

19 | Reliability versus performance for critical applications
- Girault, Saule, et al.
- 2009
(Show Context)
Citation Context ...ution is the model under study in this work, and it consists in re-executing a task that does not meet the reliability constraint; it was also studied in [25, 24, 17]; (ii) replication was studied in =-=[1, 12]-=-; this model consists in executing the same task on several processors simultaneously, in order to meet the reliability constraints; and (iii) checkpointing consists in "saving" the work done at some ... |

16 | Tradeoff exploration between reliability power consumption and execution time
- Assayad, Girault, et al.
- 2011
(Show Context)
Citation Context ...ution is the model under study in this work, and it consists in re-executing a task that does not meet the reliability constraint; it was also studied in [25, 24, 17]; (ii) replication was studied in =-=[1, 12]-=-; this model consists in executing the same task on several processors simultaneously, in order to meet the reliability constraints; and (iii) checkpointing consists in "saving" the work done at some ... |

15 |
A Power Supply Selector for Energy- and Area-Efficient Local Dynamic Voltage Scaling
- Miermont, Vivet, et al.
- 2007
(Show Context)
Citation Context ...inite number of different speeds (f1, ..., fm). It can also change its speed during a computation (hopping between different voltages, and hence speeds). Any rational speed can therefore be simulated =-=[15]-=-. The energy consumed during the execution of one task is the sum, on each time interval with constant speed f , of the energy consumed during this interval at speed f . Energy-aware scheduling aims a... |

13 |
Reclaiming the energy of a schedule: models and algorithms
- Aupy, Benoit, et al.
- 2011
(Show Context)
Citation Context ...nd it is well known to be NP-complete [7]. Since the introduction of DVFS, many papers have dealt with the optimization of energy consumption while enforcing a deadline, i.e., a bound on the makespan =-=[4, 6, 8, 3]-=-. There are many situations in which the mapping of the task graph is given, say by an ordered list of tasks to execute on each processor, and we do not have the freedom to change the assignment of a ... |

13 |
Scheduling parallel programs assuming preallocation
- Rayward-Smith, Burton, et al.
- 1995
(Show Context)
Citation Context ...to change the assignment of a given task. Such a problem occurs when optimizing for legacy applications, or accounting for affinities between tasks and resources, or even when tasks are pre-allocated =-=[19]-=-, for example for security reasons. While it is not possible to change the allocation of a task, it is possible to change its speed. This technique, which consists in exploiting the slack due to workl... |

12 |
Energy efficient scheduling techniques for real-time embedded systems
- Prathipati
- 2004
(Show Context)
Citation Context ...t is not possible to change the allocation of a task, it is possible to change its speed. This technique, which consists in exploiting the slack due to workload variations, is called slack reclaiming =-=[13, 18]-=-. In our previous work [3], assuming that the mapping and a deadline are given, we have assessed the impact of several speed variation models on the complexity of the problem of minimizing the energy ... |

9 | Random graph generation for scheduling simulations
- Cordeiro, Mounie, et al.
- 2010
(Show Context)
Citation Context ...er with additional results that were omitted due to lack of space). 16 6.1 Simulation settings In order to evaluate the heuristics, we have generated DAGs using the random DAG generation library GGEN =-=[9]-=-. Since GGEN does not assign a weight to the tasks of the DAGs, we use a function that gives a random float value in the interval [0, 10]. Each simulation uses a DAG with 100 nodes and 300 edges. We o... |

3 | Source code and data. http://gaupy.org/tri-criteria-scheduling - Aupy |

3 |
GGEN, a library of Random Graph Generation. http://ligforge.imag.fr/projects/ggen
- Perarnau
(Show Context)
Citation Context ...that were omitted due to lack of space, are publicly available at [2]. 7.1 Simulation settings In order to evaluate the heuristics, we have generated DAGs using the random DAG generation library GGEN =-=[15]-=-. Since GGEN does not give a weight to the tasks of the DAGs, we use a function that gives a random float value in the interval [0, 10]. Each simulation uses a DAG with 100 nodes and 300 edges. We obs... |