Dependence graph

Tensometer indications illustrating the extension of the reference element constitute one coordinate of the dependence graphs of the indications and the size of stress, and the Wirotest indications constitute the second coordinate. 

We now discuss the structure of this book, which is given as a structure and dependency graph in Fig. 1.29. The graph does not contain all nodes. 

Fig. 1.29. A dependency graph describing the structure of this book...

Fig. 3 shows a sample program as well as its dependency graphs whose arcs are additionally labeled with the register shared between producer and consumer. The dependency graph of a program P can be viewed as a skeleton of a partial order

execution order of Ps instructions if i < j, then the execution of j cannot be initiated before the execution of i has completed. It also makes explicit the parallelism inherent in P two instructions can (up to structural hazards) be executed concurrently iff they are unordered w.r.t. minimal elements of this partial order are the instructions j such that there exists no instruction i < j. 

Observe that the dependency graph pays no attention to the identity of the registers in which instructions store their results, except for their use in identifying the producer-consumer relations between instructions. For example, the graph allows the execution of le after I and before /4, even though both 11 and Iq write to F and U needs the value produced by /i. In fact, the dependency graph can be interpreted as denoting a set of processes - the... 

We now describe the concept of data-driven execution informally using the sample dependency graph. This can be viewed as restating the well-known concept of a data-driven execution of functional languages as implemented by data-flow architectures. 

The dependency checker monitors notifications by the Eclipse resources plug-in regarding modifications of files in the workspace. Following notifications, links entering and leaving the modified resource are checked for validity, and the dependency graph is updated. 

Dependency checker notifies other elements of changes to the dependency graph. The elements interested in receiving notifications must register with the dependency checker service in order to receive notifications. 

We will focus on examination of designed model for detection period within the range from 24 hours to one hour. Than we can design dependence graph with relationship between detection period and unavailability of the whole system mentioned. 

Definition 3.1 A schedule is time-minimal when the number of time-steps is equal to the length of a longest path in the dependence graph (which is clearly the minimal time needed to achieve the computation). 

We will assume here that the (non-uniform) dependence graph of the APP has already been extracted from the initial textual specification. In practice, this step can be performed automatically from applicative languages in a relatively simple way, as explained briefly in chapter 6 or from procedural nested loop notations expressed in any standard programming language, with more complex procedures, as discussed in chapters 4 and 5. 

The dependence graph corresponding to the APP algorithm contains opposite dependence vectors for instance, node (3,2,2) depends on node (2,2,2) hence the dependence vector (1,0,0). But node (1,2,2) also depends upon node (2,2,2) hence the dependence vector (-1,0,0). The existence of these two opposite... 

It preserves the inherent regularity of the dependence graph by allowing a regular paving of the array with rectangles. 

We will illustrate the entire method on the example of the APP. The initial dependence graph and the computation domain after space-time mapping have been presented in section 5. Assuming that we want a compression factor c = 3, the vector projection s is chosen in the plane (i, j) such that the input data are projected onto a line which will become one of the boundaries of the array. To... 

Unfortunately, an NLP does not explicitly show the parallelism of the computations. Therefore, the first step in the design trajectory is to convert the NLP into a dependence graph (see chapter 2) [4]. The resulting DG will have a node for each instance of the calculation of a function, e.g., Floyd in the example below. Its edges will represent the passing of arguments between those functional nodes and hence implement function calls. We will discuss the conversion step in more detail in section 5. Similar functionality is provided in the approach of chapter 5 but for a partly different target domain. 

Figure 9 Transformed dependence graph of the Floyd-Steinberg algorithm, given that X = [3,4] and P = [0,1]. ...

At this point, we have obtained a dependence graph consisting of regular subgraphs in each of which a different operation takes place. If these parts have to be mapped to the same array processor, a scheduling and memory allocation problem arises, which we will now address. 

P. Wielage. The partitioning of piecewise regular dependence graphs. Master s Thesis, nr 91-109, Delft University of Technology, January 1992. 

The first goal in our methodology is to transform an algorithm given in nested-loop form, which may include non-constant dependencies, to an equivalent URE with localized parametric DVs. The motivation for this starting point is also discussed in chapter 4. The applicability of such a transformation is restricted by the complexity of the index functions of the feedback variables. Therefore, our attention is focused on WSACs [20], which are characterized by identical linear index functions of the feedback variable. In this approach UREs are derived directly, in contrast to the technique described in chapter 4 where the dependence graph (DG) is extracted. 

Let a variable instance computed at a point ii use the value of a variable instance generated at another point i2> The vector d = i2-ii is called dependence vector. The dependence graph (DG) is a directed graph, where each node corresponds to a point i G and each edge corresponds to a DV joining two dependent points of the index space. 

These data- and control-flow transformations are based on an extended poly-hedral dependence graph (PDG) model [23] (see also chapter 7), in terms of which the actual optimization problem is defined and the transformations are performed. In this section, a short overview is given of the main concepts of the PDG. Detailed information can be found elsewhere [23, 22]. 

Figure 4 shows a simplified dependency graph for EXAMPLE, formed by combining and simplifying the DFG and CFG. It contains only the essential operation dependencies, i.e., data dependencies (such as between operations 5 and 7), resource conflicts (operations 3 and 4... 

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