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abeled with its name. onsider the following digraph D, in which each vertex is V6 V5 V1 V4 V2 V3 Now consider the directed network (D, w), where w: A(D) → R with W(V₁V₂) = 4, W(V1V6): =−1, W(v₂V3) = 1, w(V3V2) = 2, W(V3V4) = 2, W(V4V3) = 1, W(V5V4) = 1, w(v6V₂) = 4, w(v6v5) = 1. W(V2V4) = -2 w(V5V₂) = 2 Recall that Dijkstra's algorithm may fail to find shortest directed paths in the presence of negative weights. Illustrate this fact by giving vertices u, v € V(D) such that Dijkstra's algorithm fails to find a shortest directed u-v-path in (D, w). Explain your reasoning.

abeled with its name. onsider the following digraph D, in which each vertex is V6 V5 V1 V4 V2 V3 Now consider the directed network (D, w), where w: A(D) → R with W(V₁V₂) = 4, W(V1V6): =−1, W(v₂V3) = 1, w(V3V2) = 2, W(V3V4) = 2, W(V4V3) = 1, W(V5V4) = 1, w(v6V₂) = 4, w(v6v5) = 1. W(V2V4) = -2 w(V5V₂) = 2 Recall that Dijkstra's algorithm may fail to find shortest directed paths in the presence of negative weights. Illustrate this fact by giving vertices u, v € V(D) such that Dijkstra's algorithm fails to find a shortest directed u-v-path in (D, w). Explain your reasoning.

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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Question 3 labeled with its name. Consider the following digraph D, in which each vertex is - V6 V5 V1 V4 V2 V3 Now consider the directed network (D, w), where w: A(D) → R with w(v₁v₂) = 4, W(V₁V6) = -1, W(V₂V3) = 1, W(V3V₂) = 2, W(V3V4) = 2, W(V4V3) = 1, W(V5V4) 1, w(V6V₂) = 4, W(V6V5) 1. - W(V2V4) W(V5V₂) = -2 = 2 Recall that Dijkstra’s algorithm may fail to find shortest directed paths in the presence of negative weights. Illustrate this fact by giving vertices u, v € V(D) such that Dijkstra's algorithm fails to find a shortest directed u-v-path in (D, w). Explain your reasoning.
Transcribed Image Text:Question 3 labeled with its name. Consider the following digraph D, in which each vertex is - V6 V5 V1 V4 V2 V3 Now consider the directed network (D, w), where w: A(D) → R with w(v₁v₂) = 4, W(V₁V6) = -1, W(V₂V3) = 1, W(V3V₂) = 2, W(V3V4) = 2, W(V4V3) = 1, W(V5V4) 1, w(V6V₂) = 4, W(V6V5) 1. - W(V2V4) W(V5V₂) = -2 = 2 Recall that Dijkstra’s algorithm may fail to find shortest directed paths in the presence of negative weights. Illustrate this fact by giving vertices u, v € V(D) such that Dijkstra's algorithm fails to find a shortest directed u-v-path in (D, w). Explain your reasoning.
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