• Task-dependency graph determines which tasks can execute in parallel and which must wait for some others to finish at a given stage. 2. Good mapping must ensure that computations and interactions among processes at each stage of execution are well balanced.

• Task interaction graph: an undirected graph that captures the pattern of interaction among tasks • Note that task interaction graphs represent data dependencies, whereas task dependency

Jul 31, 2023 · The parallelism that is described with the task dependency graph where each task is an independent task is known as task parallelism. The task graph model is majorly used for the implementation of parallel quick sort, a parallel algorithm based on divide and conquer.

• Identify tasks. • Analyze with task dependency & interaction graphs. • Map tasks to processes. • Now properties of tasks that affect a good mapping. • Task generation, size of tasks, and size of data.

What does a task dependency graph look like for this case? What is the shortest parallel execution time for the graph? How many processors are needed to achieve the minimum time?

Partitioning the input data and associating a task with each partition of the input data. Example: Input Data Decomposition. Count the frequency of itemsets in database transactions. Applicable for problems which can be solved by multi-stage computations such that the output of one stage is the input to the subsequent stage.

A task-dependency graph is a directed acyclic graph in which the nodes represent tasks and the directed edges indicate the dependencies amongst them. The task corresponding to a node can be executed when all tasks connected to this node by incoming edges have completed.

•Task = indivisible sequential unit of computation •A decomposition can be illustrated in the form of a directed graph with nodes corresponding to tasks and edges indicating that the result of one task is required for processing the next. Such a graph is called a task dependency graph.

Tasks and dependency graphs ä First issue: identify \tasks" considered as indivisible units of work. \Fine-grain" parallelism: tasks are grouped in very small units, e.g., at the level of artithmetic operations. \Coarse grain" parallelism: tasks are bigger. ä Tasks depend on each other : the result of one task may be required by another task.

Break down the problem using the Task Decomposition, Group Tasks and Order Tasks patterns to decompose the tasks and analyze the dependencies and non-dependencies between them (see: Patterns for Parallel Programming, Chapter 3 (2)). In summary: