Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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### Application of Backflow Algorithm to a Directed Graph This diagram represents a directed graph (digraph) with tasks (T1 to T10) and their respective processing times in parentheses. The aim is to apply the backflow algorithm to determine the critical time for specific tasks within this network. #### Diagram Overview: - **Tasks and Times**: - T1 (3) - T2 (2) - T3 (8) - T4 (11) - T5 (12) - T6 (10) - T7 (9) - T8 (4) - T9 (6) - T10 (5) - **Connections**: - The arrows indicate dependency and flow direction from one task to another. - T1 connects to T5. - T2 connects to T6. - T5 connects to T9. - Tasks T6, T8, and T10 are subsequent connections before reaching the "End". - T3 connects to T7. - T4 is a task that stands independently before reaching the "End". #### Calculating Critical Time: - **Purpose**: Calculate the critical time for Task 5 and Task 2 using the backflow algorithm. - **Formulas**: - The backward pass evaluates the longest path from end to start, determining critical times through reverse calculation from the "End" node. - Task duration and dependencies are considered to find potential delays affecting the overall project completion time. #### Critical Time Boxes: - **Task 5 Critical Time**: ________ - **Task 2 Critical Time**: ________ By evaluating the backward paths from each task to the "End," fill in the critical times in the designated boxes. This process aids in optimizing project schedules and identifying key dependency paths within project management scenarios.
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Transcribed Image Text:### Application of Backflow Algorithm to a Directed Graph This diagram represents a directed graph (digraph) with tasks (T1 to T10) and their respective processing times in parentheses. The aim is to apply the backflow algorithm to determine the critical time for specific tasks within this network. #### Diagram Overview: - **Tasks and Times**: - T1 (3) - T2 (2) - T3 (8) - T4 (11) - T5 (12) - T6 (10) - T7 (9) - T8 (4) - T9 (6) - T10 (5) - **Connections**: - The arrows indicate dependency and flow direction from one task to another. - T1 connects to T5. - T2 connects to T6. - T5 connects to T9. - Tasks T6, T8, and T10 are subsequent connections before reaching the "End". - T3 connects to T7. - T4 is a task that stands independently before reaching the "End". #### Calculating Critical Time: - **Purpose**: Calculate the critical time for Task 5 and Task 2 using the backflow algorithm. - **Formulas**: - The backward pass evaluates the longest path from end to start, determining critical times through reverse calculation from the "End" node. - Task duration and dependencies are considered to find potential delays affecting the overall project completion time. #### Critical Time Boxes: - **Task 5 Critical Time**: ________ - **Task 2 Critical Time**: ________ By evaluating the backward paths from each task to the "End," fill in the critical times in the designated boxes. This process aids in optimizing project schedules and identifying key dependency paths within project management scenarios.
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