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Let {A,..., H} be a set of tasks that we must complete. The following DAG de- scribes which tasks must be done before others, where there is an arrow from S to Tiff S must be done before T. A D B E F

Let {A,..., H} be a set of tasks that we must complete. The following DAG de- scribes which tasks must be done before others, where there is an arrow from S to Tiff S must be done before T. A D B E F

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Discrete Math

Let \(\{A, \ldots, H\}\) be a set of tasks that we must complete. The following Directed Acyclic Graph (DAG) describes which tasks must be done before others, where there is an arrow from \(S\) to \(T\) if and only if \(S\) must be done before \(T\). The diagram is a directed graph with the following edges: - \(A \rightarrow D\) - \(B \rightarrow E\) - \(B \rightarrow F\) - \(B \rightarrow G\) - \(C \rightarrow F\) - \(D \rightarrow E\) - \(F \rightarrow H\) (a) Write the longest chain. (b) Write the longest antichain. (c) If we allow parallel scheduling, and each task takes 1 minute to complete, what is the minimum amount of time needed to complete all tasks?
Transcribed Image Text:Let \(\{A, \ldots, H\}\) be a set of tasks that we must complete. The following Directed Acyclic Graph (DAG) describes which tasks must be done before others, where there is an arrow from \(S\) to \(T\) if and only if \(S\) must be done before \(T\). The diagram is a directed graph with the following edges: - \(A \rightarrow D\) - \(B \rightarrow E\) - \(B \rightarrow F\) - \(B \rightarrow G\) - \(C \rightarrow F\) - \(D \rightarrow E\) - \(F \rightarrow H\) (a) Write the longest chain. (b) Write the longest antichain. (c) If we allow parallel scheduling, and each task takes 1 minute to complete, what is the minimum amount of time needed to complete all tasks?
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