Figure 319 The three major graph models and the relationships among them in Visual Studio .NET

Drawer Denso QR Bar Code in Visual Studio .NET Figure 319 The three major graph models and the relationships among them
Figure 319 The three major graph models and the relationships among them
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GRAPH REPRESENTATIONS
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352 Motivations and Limitations This subsection discusses the motivations for the adoption of the task graph model for task scheduling, which is accompanied by a critical discussion of its limitations Basically, this goal is achieved by summarizing and comparing the principal properties of the presented graph models Motivations So far, this chapter has demonstrated that the abstraction of a program as a graph can very well capture the dependence and communication structure of a program The task graph model has several properties that make it particularly suitable for task scheduling
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General It is desirable that the graph model is as general as possible, in terms of the computation types, and the task graph is such a model In comparison, the ow graph is restricted to iterative computations with uniform communications (otherwise it is not accurate) Simple The task graph s focus on communications, which correspond to real data dependence, permits task scheduling to concentrate on these essential precedence constraints Other dependences re ected in the DG can be eliminated and are not inherent to the represented computation Modeling of Computation and Communication Costs Scheduling algorithms for modern parallel systems must be aware of the computation and communication costs It is therefore crucial that they are represented in the graph model; hence, a DG does not suf ce Close Relationship to Other Models The previous section outlined the various relationships between the discussed models In connection with a conversion or transformation, techniques and algorithms based on the task graph can be employed for other models
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Limitations The task graph as a general model does not provide any mechanism to ef ciently represent an iterative computation
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Iterative Computations For iterative computations, the size of the task graph depends on the number of iterations, which directly in uences the memory consumption and the processing time of task scheduling algorithms With the loss of regularity information in the task graph, scheduling algorithms also cannot bene t from the inherent regularity of cyclic computations Furthermore, if the number of iterations is only known at runtime, the task graph cannot be constructed for the general case Still, scheduling techniques for cyclic computations (Sandnes and Megson [164], Sandnes and Sinnen [166], Yang and Fu [208]) do use the task graph and associated techniques, for example, to represent the iterative kernel
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CONCLUDING REMARKS
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Another limitation is not a particular limitation of the task graph, but of all models covered in this chapter In fact, it was already introduced during the de nition of the general graph model in Section 32
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Static Model The graph models according to De nition 37, to which the task graph model belongs, do not exhibit conditional statements of the code; that is, there is no branching These control dependences are either transformed into data dependences or encapsulated within a node (see Section 32)
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353 Summary The task graph is the graph model of choice for task scheduling It clearly exhibits the task and communication structure of a program, while also re ecting the computation and communication costs Its properties were summarized in the previous section, when analyzing the motivations for the model s choice and its limitations The general nature of the task graph, together with the typically coarse granularity of the represented tasks, indicates the adequacy of employing the task graph for distributed parallel systems with SPMD or MIMD streams 4 returns to the task graph model after establishing a basic understanding of the task scheduling problem on parallel systems It is there that the task graph model and its properties are examined further in the context of task scheduling Also, 4 addresses the computation and communication costs associated with the nodes and the edges of the task graph, respectively Until now, the node and edge weights were introduced only as abstract notations of computation and communication costs Evidently, such costs are related to the target parallel system on which the program represented by the task graph is executed Thus, it is necessary to de ne the target parallel system model, before the concept of costs in the task graph can be substantiated
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36 CONCLUDING REMARKS This chapter presented and analyzed in depth the three major graph models for the representation of computer programs: dependence graph, ow graph, and task graph It started with the fundamental concepts of graph theory and then formulated a common foundation for graph models representing computer programs With this background, the three models and their properties were discussed While this chapter serves as an introduction to graph models for program representation, its objective was to introduce and analyze the task graph model of task scheduling This broad approach was deemed crucial in order to establish a comprehensive understanding of the task graph It was shown that the task graph model inherits the structure of the dependence graph and many of its properties Furthermore, the ow graph, as a concise representation of iterative computation, was related to the task graph by means of transformations and conversions, discussed in
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