Dijkstra's algorithm for computing lowest cost paths from a single source node is always correct for graphs without negative-cost edges. If a graph has negative-cost edges, the algorithm might or might not give the right answer. For the directed weighted graph below, list all nodes which Dijkstra's algorithm produces the wrong path and write the correct lowest-cost path. -2 7 -1 A B.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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### Dijkstra's Algorithm and Negative Cost Edges

Dijkstra's algorithm for computing lowest cost paths from a single source node is always correct for graphs without negative-cost edges. If a graph has negative-cost edges, the algorithm might or might not give the right answer. For the directed weighted graph below, list all nodes which Dijkstra's algorithm produces the wrong path and write the correct lowest-cost path.

#### Graph Description
In the graph provided:

- Node A has two directed edges:
  - To node B with a weight of 7.
  - To node C with a weight of 3.
  
- Node B has a directed edge:
  - To node D with a weight of -2.
  
- Node C has a directed edge:
  - To node D with a weight of 3.
  
- Node D has a directed edge:
  - To node E with a weight of -1.


#### Analysis Questions
1. The correct lowest-cost path from A to E should be:
   *Answer hidden*
   
2. The lowest-cost path from A to E that is produced from Dijkstra's algorithm (*Answer hidden*):

*Note: The answers are intentionally hidden for educational purposes in this transcription to encourage problem-solving.*
Transcribed Image Text:### Dijkstra's Algorithm and Negative Cost Edges Dijkstra's algorithm for computing lowest cost paths from a single source node is always correct for graphs without negative-cost edges. If a graph has negative-cost edges, the algorithm might or might not give the right answer. For the directed weighted graph below, list all nodes which Dijkstra's algorithm produces the wrong path and write the correct lowest-cost path. #### Graph Description In the graph provided: - Node A has two directed edges: - To node B with a weight of 7. - To node C with a weight of 3. - Node B has a directed edge: - To node D with a weight of -2. - Node C has a directed edge: - To node D with a weight of 3. - Node D has a directed edge: - To node E with a weight of -1. #### Analysis Questions 1. The correct lowest-cost path from A to E should be: *Answer hidden* 2. The lowest-cost path from A to E that is produced from Dijkstra's algorithm (*Answer hidden*): *Note: The answers are intentionally hidden for educational purposes in this transcription to encourage problem-solving.*
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