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precedence relations. One exam as vertices and edges represents I, then there is an edge from ver can easily be done by performing

precedence relations. One exam as vertices and edges represents I, then there is an edge from ver can easily be done by performing

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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II. Read each problem carefully and present an algorithm with the required running-time to solve each problem. 1. In class we discussed that directed acyclic graphs (DAG) can be used to represent dependency/precedence relations. One example is modeling task dependency where tasks are represented as vertices and edges represents direct dependencies between tasks, e.g., if task T requires task T, then there is an edge from vertex i to vertex j. Arranging tasks with respect to their dependencies can easily be done by performing topological sort to the DAG. a. Describe an algorithm that runs in O(n + m) time that given two tasks, T, and I₁, determines if task T, can be performed without performing task T₁. Note that I, is not required if it is not a direct or indirect dependency of T. Task I, is an indirect dependency of task T, if there is no edge from T, to T, but I must appear before 7, in the topological order. b. Describe an algorithm that runs in O(n + m) time that given a task T₁, outputs the minimum possible position of tasks T, in any topological order.
Transcribed Image Text:II. Read each problem carefully and present an algorithm with the required running-time to solve each problem. 1. In class we discussed that directed acyclic graphs (DAG) can be used to represent dependency/precedence relations. One example is modeling task dependency where tasks are represented as vertices and edges represents direct dependencies between tasks, e.g., if task T requires task T, then there is an edge from vertex i to vertex j. Arranging tasks with respect to their dependencies can easily be done by performing topological sort to the DAG. a. Describe an algorithm that runs in O(n + m) time that given two tasks, T, and I₁, determines if task T, can be performed without performing task T₁. Note that I, is not required if it is not a direct or indirect dependency of T. Task I, is an indirect dependency of task T, if there is no edge from T, to T, but I must appear before 7, in the topological order. b. Describe an algorithm that runs in O(n + m) time that given a task T₁, outputs the minimum possible position of tasks T, in any topological order.
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