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In the Examples section of the Task Decomposition pattern we discuss decomposing the matrix multiplication C = A B into tasks, each corresponding to the update of one element in C The memory organization of most modern computers, however, favors larger grained tasks such as updating a block of C, as described in the Examples section of the Data Decomposition pattern Mathematically, this is equivalent to grouping the elementwise update tasks into groups corresponding to blocks, and grouping the tasks this way is well suited to an optimum utilization of system memory
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35 THE ORDER TASKS PATTERN
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Problem Given a way of decomposing a problem into tasks and a way of collecting these tasks into logically related groups, how must these groups of tasks be ordered to satisfy constraints among tasks Context This pattern constitutes the second step in analyzing dependencies among the tasks of a problem decomposition The first step, addressed in the Group Tasks pattern, is to group tasks based on constraints among them The next step, discussed here, is to find and correctly account for dependencies resulting from constraints on the order of execution of a collection of tasks Constraints among tasks fall into a few major categories:
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Temporal dependencies, that is, constraints placed on the order in which a collection of tasks executes Requirements that particular tasks must execute at the same time (for example, because each requires information that will be produced by the others) Lack of constraint, that is, total independence Although this is not strictly speaking a constraint, it is an important feature of a set of tasks because it means they can execute in any order, including concurrently, and it is important to clearly note when this holds
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The purpose of this pattern is to help find and correctly account for dependencies resulting from constraints on the order of execution of a collection of tasks Solution There are two goals to be met when identifying ordering constraints among tasks and defining a partial order among task groups
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The ordering must be restrictive enough to satisfy all the constraints so that the resulting design is correct The ordering should not be more restrictive than it needs to be Overly constraining the solution limits design options and can impair program efficiency; the fewer the constraints, the more flexibility you have to shift tasks around to balance the computational load among PEs First look at the data required by a group of tasks before they can execute After this data has been identified, find the task group that creates it and an ordering constraint will be apparent For example, if one group of tasks (call it A) builds a complex data structure and another group (B) uses it, there is a sequential ordering constraint between these groups When these two groups are combined in a program, they must execute in sequence, first A and then B Also consider whether external services can impose ordering constraints For example, if a program must write to a file in a certain order, then these file I/O operations likely impose an ordering constraint Finally, it is equally important to note when an ordering constraint does not exist If a number of task groups can execute independently, there is a much greater opportunity to exploit parallelism, so we need to note when tasks are independent as well as when they are dependent
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To identify ordering constraints, consider the following ways tasks can depend on each other
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Regardless of the source of the constraint, we must define the constraints that restrict the order of execution and make sure they are handled correctly in the resulting algorithm At the same time, it is important to note when ordering constraints are absent, since this will give valuable flexibility later in the design Examples
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