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37
Complexity Results for Throughput and Latency Optimization of Replicated and Dataparallel Workflow
 ALGORITHMICA
, 2007
"... Mapping applications onto parallel platforms is a challenging problem, even for simple application patterns such as pipeline or fork graphs. Several antagonist criteria should be optimized for workflow applications, such as throughput and latency (or a combination). In this paper, we consider a si ..."
Abstract

Cited by 19 (16 self)
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Mapping applications onto parallel platforms is a challenging problem, even for simple application patterns such as pipeline or fork graphs. Several antagonist criteria should be optimized for workflow applications, such as throughput and latency (or a combination). In this paper, we consider a simplified model with no communication cost, and we provide an exhaustive list of complexity results for different problem instances. Pipeline or fork stages can be replicated in order to increase the throughput by sending consecutive data sets onto different processors. In some cases, stages can also be dataparallelized, i.e. the computation of one single data set is shared between several processors. This leads to a decrease of the latency and an increase of the throughput. Some instances of this simple model are shown to be NPhard, thereby exposing the inherent complexity of the mapping problem. We provide polynomial algorithms for other problem instances. Altogether, we provide solid theoretical foundations for the study of monocriterion or bicriteria mapping optimization problems.
Mapping Linear Workflows with Computation/Communication Overlap
"... This paper presents theoretical results related to mapping and scheduling linear workflows onto heterogeneous platforms. We use a realistic architectural model with bounded communication capabilities and full computation/communication overlap. This model is representative of current multithreaded s ..."
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Cited by 10 (8 self)
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This paper presents theoretical results related to mapping and scheduling linear workflows onto heterogeneous platforms. We use a realistic architectural model with bounded communication capabilities and full computation/communication overlap. This model is representative of current multithreaded systems. In these workflow applications, the goal is often to maximize throughput or to minimize latency. We present several complexity results related to both these criteria. To be precise, we prove that maximizing the throughput is NPcomplete even for homogeneous platforms and minimizing the latency is NPcomplete for heterogeneous platforms. Moreover, we present an approximation algorithm for throughput maximization for linear chain applications on homogeneous platforms, and an approximation algorithm for latency minimization for linear chain applications on all platforms where communication is homogeneous (the processor speeds can differ). In addition, we present algorithms for several important special cases for linear chain applications. Finally, we consider the implications of adding feedback loops to linear chain applications.
Performance and energy optimization of concurrent pipelined applications
, 2009
"... In this paper, we study the problem of finding optimal mappings for several independent but concurrent workflow applications, in order to optimize performancerelated criteria together with energy consumption. Each application consists in a linear chain application with several stages, and processes ..."
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Cited by 9 (9 self)
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In this paper, we study the problem of finding optimal mappings for several independent but concurrent workflow applications, in order to optimize performancerelated criteria together with energy consumption. Each application consists in a linear chain application with several stages, and processes successive data sets in pipeline mode, from the first to the last stage. We study the problem complexity on different target execution platforms, ranking from fully homogeneous platforms to fully heterogeneous ones. The goal is to select an execution speed for each processor, and then to assign stages to processors, with the aim of optimizing several concurrent optimization criteria. There is a clear tradeoff to reach, since running faster and/or more processors leads to better performance, but the energy consumption is then very high. Energy savings can be done at the price of a lower performance, by reducing processor speeds or enrolling fewer resources.. We consider two mapping strategies: in onetoone mappings, a processor is assigned a single stage, while in interval mappings, a processor may process an interval of consecutive stages of the same application. For both mapping strategies and all platform types, we establish the complexity of several
Mapping Filtering Streaming Applications With Communication Costs
, 2009
"... In this paper, we explore the problem of mapping filtering streaming applications on largescale homogeneous platforms, with a particular emphasis on communication models and their impact. Filtering application are streaming applications where each node also has a selectivity which either increases ..."
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Cited by 6 (5 self)
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In this paper, we explore the problem of mapping filtering streaming applications on largescale homogeneous platforms, with a particular emphasis on communication models and their impact. Filtering application are streaming applications where each node also has a selectivity which either increases or decreases the size of its input data set. This selectivity makes the problem of scheduling these applications more challenging than the more studied problem of scheduling “nonfiltering ” streaming workflows. We identify three significant realistic communication models. For each of them, we address the complexity of the following important problems: 1. Given an execution graph, how can one compute the period and latency? A solution to this problem is an operation list which provides the timesteps at which each computation and each communication occurs in the system. 2. Given a filtering workflow problem, how can one compute the schedule that minimizes the period or latency? A solution to this problem requires generating both the execution graph and the associated operation list. Altogether, with three models, two problems and two objectives, we present 12 complexity results, thereby providing solid theoretical foundations for the study of filtering streaming applications. Key words: query optimization, web service, streaming application, workflow, communication model, period, latency, complexity results. 0 1
Computing the throughput of probabilistic and replicated streaming applications
 Research Report RR7182, INRIA
, 2010
"... apport de recherche ..."
Scheduling algorithms for workflow optimization
, 2009
"... Pipelined workflows are a popular programming paradigm for parallel applications. In these workflows, the computation is divided into several stages and these stages are connected to each other through firstin firstout channels. In order to execute these workflows on a parallel machine, we must fi ..."
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Cited by 6 (6 self)
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Pipelined workflows are a popular programming paradigm for parallel applications. In these workflows, the computation is divided into several stages and these stages are connected to each other through firstin firstout channels. In order to execute these workflows on a parallel machine, we must first determine the mapping of the stages onto the various processors on the machine. After finding the mapping, we must compute the schedule — the order in which the various stages execute on their assigned processors. In this paper, we explore the scheduling problem for linear workflows, assuming that the mapping is given. Linear workflows are a special case of workflows for which the dependencies between stages can be represented by a linear graph. The objective of the scheduling algorithm is either to maximize throughput or to minimize latency or both. We consider two realistic execution models: the oneport model and the multiport model. In both models, finding a schedule to minimize latency is easy. However, computing the schedule to minimize period (maximize throughput) is NPhard in the oneport model, but can be done in polynomial time in the multiport model. We also present an approximation algorithm to minimize period in the oneport model. Finally, the bicriteria problem, which consists in finding a schedule respecting a given period and a given latency, is NPhard in both models.
Mapping Filter Services on Heterogeneous Platforms
, 2008
"... In this paper, we explore the problem of mapping filtering web services on largescale heterogeneous platforms. Two important optimization criteria should be considered in such a framework. The period, which is the inverse of the throughput, measures the rate at which data sets can enter the system. ..."
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Cited by 5 (4 self)
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In this paper, we explore the problem of mapping filtering web services on largescale heterogeneous platforms. Two important optimization criteria should be considered in such a framework. The period, which is the inverse of the throughput, measures the rate at which data sets can enter the system. The latency measures the response time of the system in order to process one single data set entirely. Both criteria are antagonistic. For homogeneous platforms, the complexity of period minimization is already known [14]; we derive an algorithm to solve the latency minimization problem, and we provide a bicriteria algorithm which minimizes latency without exceeding a prescribed value for the period. However, when adding heterogeneity to the platform, we prove that minimizing the period or the latency becomes NPhard. We provide an integer linear program to solve both problems in the heterogeneous case. For period minimization on heterogeneous platforms, we design some efficient polynomial time heuristics and we assess their relative and absolute performance through a set of experiments. For small problem instances, the results are very close to the optimal solution returned by the integer linear program.
Reliability and performance optimization of pipelined realtime systems
, 2009
"... We consider pipelined realtime 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 inputoutpu ..."
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Cited by 4 (4 self)
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We consider pipelined realtime 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 inputoutput 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 NPhardness complexity results, and optimal mapping algorithms for polynomial problem instances. Keywords: Pipelined realtime systems, interval mapping, multicriteria (reliability, latency, period) optimization, complexity results, dynamic programming algorithm. 1 Reliability
Y.: Filter placement on a pipelined architecture
 In: International Symposium on Parallel and Distributed Processing
, 2009
"... In this paper, we explore the problem of mapping filtering query services on chains of heterogeneous processors. Two important optimization criteria should be considered in such a framework. The period, which is the inverse of the throughput, measures the rate at which data sets can enter the system ..."
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Cited by 4 (3 self)
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In this paper, we explore the problem of mapping filtering query services on chains of heterogeneous processors. Two important optimization criteria should be considered in such a framework. The period, which is the inverse of the throughput, measures the rate at which data sets can enter the system. The latency measures the response time of the system in order to process one single data set entirely. We provide a comprehensive set of complexity results for period and latency optimization problems, with proportional or arbitrary computation costs, and without or with communication costs. We present polynomial algorithms for problems whose dependence graph is a linear chain (hence a fixed ordering of the filtering services). For independent services, the problems are all NPcomplete except latency minimization with proportional computation costs, which was shown polynomial in [6]. 1
On the Complexity of Mapping Pipelined Filtering Services on Heterogeneous Platforms
, 2008
"... In this paper, we explore the problem of mapping filtering services on largescale heterogeneous platforms. Two important optimization criteria should be considered in such a framework. The period, which is the inverse of the throughput, measures the rate at which data sets can enter the system. The ..."
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Cited by 3 (3 self)
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In this paper, we explore the problem of mapping filtering services on largescale heterogeneous platforms. Two important optimization criteria should be considered in such a framework. The period, which is the inverse of the throughput, measures the rate at which data sets can enter the system. The latency measures the response time of the system in order to process one single data set entirely. Both criteria are antagonistic. For homogeneous platforms, the complexity of period minimization is already known [1]; we derive an algorithm to solve the latency minimization problem in the general case with service precedence constraints; for independent services we also show that the bicriteria problem (latency minimization without exceeding a prescribed value for the period) is of polynomial complexity. However, when adding heterogeneity to the platform, we prove that minimizing the period or the latency becomes NPhard, and that these problems cannot be approximated by any constant factor (unless P=NP). The latter results hold true even for independent services. We provide an integer linear program to solve both problems in the heterogeneous case with independent services. For period minimization on heterogeneous platforms, we design some efficient polynomial time heuristics and we assess their relative and absolute performance through a set of experiments. For small problem instances, the results are very close to the optimal solution returned by the integer linear program.