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Identifying parallelism
A formal way to identify parallelism in an activity is to draw a task dependence graph in a directed graph in which each vertex represents a task to be completed. An edge from vertex u to vertex means that task u must be completed before task v begins, so that task v "depends on" u. If there is no path from u to v, then the tasks are independent and may be performed concurrently. Consider the following problem: Alice is the leader of a crew of workers who maintain a large estate. There are four principal tasks: mowing the lawns, pruning the trees and hedges, repairing the fences, and inspecting the work to ensure it has all been done satisfactorily. Mowing must be completed before the work is inspected, as must the pruning and fence repair. The estate has a security system which must be switched off before work commences (i.e. before Alice and her team arrives), and switched on again after the team leaves.
Since mowing is done first and then all team members start the work simuntaneosly and Alice can only inspect after each has finished their task the time taken by the slowest team members will be seen here.
Harriert/Bert/Credessia and Edgar take 3 hrs each to complete their task.
The manual work starts at 10.00 AM so the inspection will start 3+3 =6 hrs after that.
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