In this paper we consider the operator mapping problem for in-network stream processing applications. In-network stream processing consists in applying a tree of operators in steady-state to multiple data objects that are continually updated at various locations on a network. Examples of in-network stream processing include the processing of data in a sensor network, or of continuous queries on distributed relational databases. We study the operator mapping problem in a “constructive ” scenario, i.e., a scenario in which one builds a platform dedicated to the application by purchasing processing servers with various costs and capabilities. The objective is to minimize the cost of the platform while ensuring that the application achieves a minimum steady-state throughput. The first contribution of this paper is the formalization of a set of relevant operator-placement problems, and a proof that even simple versions of the problem are NP-complete. Our second contribution is the design of several polynomial time heuristics, which are evaluated via extensive simulations and compared to theoretical bounds for optimal solutions.

We consider pipelined real-time systems, commonly found in assembly lines, consisting of a chain of tasks executing on a distributed platform. Their processing is pipelined: each processor executes only one interval of consecutive tasks. We are therefore interested in minimizing both the input-output latency and the period. For dependability reasons, we are also interested in maximizing the reliability of the system. We therefore assign several processors to each task, so as to increase the reliability of the system. We assume that both processors and communication links are unreliable and subject to transient failures, the arrival of which follows a constant parameter Poisson law. We also assume that the failures are statistically independent events. We study several variants of this multiprocessor mapping problem with several hypotheses on the target platform (homogeneous/heterogeneous speeds and/or failure rates). We provide NP-hardness complexity results, and optimal mapping algorithms for polynomial problem instances. Keywords: Pipelined real-time systems, interval mapping, multi-criteria (reliability, latency, period) optimization, complexity results, dynamic programming algorithm. 1 Reliability

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of flow applications

This position paper advocates the need for scheduling. Even if resources at our disposal would become abundant and cheap, not to say unlimited and free (a perspective that is not granted), we would still need to assign the right task to the right device. We give several simple examples of such situations where resource selection and allocation is mandatory. Finally we expose our views on the important algorithmic challenges that need be addressed in the future. 1

Abstract. We consider the problem of scheduling an application composed of independent tasks on a fully heterogeneous master-worker platform with communication costs. We introduce a bi-criteria approach aiming at maximizing the throughput of the application while minimizing the energy consumed by participating resources. Assuming arbitrary super-linear power consumption laws, we investigate different models for energy consumption, with and without start-up overheads. Building upon closed-form expressions for the uniprocessor case, we derive optimal or asymptotically optimal solutions for both models. 1

Abstract—In this paper we study the execution of iterative applications on volatile processors such as those found on desktop grids. We develop master-worker scheduling schemes that attempt to achieve good trade-offs between worker speed and worker availability. A key feature of our approach is that we consider a communication model where the bandwidth capacity of the master for sending application data to workers is limited. This limitation makes the scheduling problem more difficult both in a theoretical sense and in a practical sense. Furthermore, we consider that a processor can be in one of three states: available, down, or temporarily preempted by its owner. This preempted state also complicates the scheduling problem. In practical settings, e.g., desktop grids, master bandwidth is limited and processors are temporarily reclaimed. Consequently, addressing the aforementioned difficulties is necessary for successfully deploying masterworker applications on volatile platforms. Our first contribution is to determine the complexity of the scheduling problem in its off-line version, i.e., when processor availability behaviors are known in advance. Even with this knowledge, the problem is NP-hard, and cannot be approximated within a factor 8/7. Our second contribution is a closed-form formula for the expectation of the time needed by a worker to complete a set of tasks. This formula relies on a Markovian assumption for the temporal availability of processors, and is at the heart of some heuristics that aim at favoring “reliable” processors in a sensible manner. Our third contribution is a set of heuristics, which we evaluate in simulation. Our results provide guidance to selecting the best strategy as a function of processor state availability versus average task duration. I.

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In this paper we consider the operator mapping problem for in-network stream processing applications. In-network stream processing consists in applying a tree of operators in steady-state to multiple data objects that are continually updated at various locations on a network. Examples of in-network stream processing include the processing of data in a sensor network, or of continuous queries on distributed relational databases. We study the operator mapping problem in a“constructive”scenario, i.e., a scenario in which one builds a platform dedicated to the application buy purchasing processing servers with various costs and capabilities. The objective is to minimize the cost of the platform while ensuring that the application achieves a minimum steady-state throughput. The first contribution of this paper is the formalization of a set of relevant operator-placement problems as linear programs, and a proof that even simple versions of the problem are NP-complete. Our second contribution

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