April 2011
Intermediate to advanced
364 pages
10h 8m
English
Content preview from Algorithms and Parallel Computing
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8.3 PARALLELIZING NSPA ALGORITHMS REPRESENTED BY A DAG
This chapter discusses techniques for extracting parallelism from DAG. Each task accepts input data and produces output results. We say a task, Ti, is dependent on task Tj if the output of Tj is used as its input to Ti. When the number of algorithm tasks is small, the algorithm can be described by a directed graph, which shows no regular patterns of interconnections among the tasks. Figure 8.1a shows an example of representing an NSPA by a DAG. The graph is characterized by two types of constructs: the nodes, which describe the tasks comprising the algorithm, and the directed edges, which describe the direction of data flow among the tasks. The edges exiting a node represent an output, and when they enter a node, they represent an input. Chapter 1 defined the types of nodes and edges in a DG: input node/edge, output node/edge, and intermediate node/edge.
Figure 8.1 shows the algorithm as drawn or sketched by the programmer or some graphing tool. Nodes 0, 1, and 2 are the only input nodes, and nodes 7 and 9 are the only output nodes. The algorithm has three primary inputs: in0, in1, and in2, and three primary outputs: out0, out1, and out2.
Example 8.1
A very popular series in computer science is the Fibonacci sequence:
An algorithm to calculate the nth Fibonacci number is given by
where N0 = 0 and N1 = 1. Draw a DAG to ...
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