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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 T₁ 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 Tj, 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 T₁. Task Tj is an indirect dependency of task T; if there is no edge from T; to T, but T, must appear before T, 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.

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 T₁ 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 Tj, 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 T₁. Task Tj is an indirect dependency of task T; if there is no edge from T; to T, but T, must appear before T, 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.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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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 Ti 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, T₁ and T₁, determines if task T₁ can be performed without performing task Tj. Note that T; is not required if it is not a direct or indirect dependency of Ti. Task T; is an indirect dependency of task T; if there is no edge from T; to T; but I must appear before T; 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 Ti 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, T₁ and T₁, determines if task T₁ can be performed without performing task Tj. Note that T; is not required if it is not a direct or indirect dependency of Ti. Task T; is an indirect dependency of task T; if there is no edge from T; to T; but I must appear before T; 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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