### Dijkstra's Algorithm (3, part 3)Consider the network shown below and Dijkstra’s link-state algorithm. Here, we are focused on computing the least cost path from node E to all other nodes using Dijkstra’s algorithm. Using the algorithm statement and its visual representation, complete the "Step 2" row in the table below to show the algorithm’s execution by matching the table entries (i), (ii), (iii), (iv), and (v) with their values. Write down your final [correct] answer, as you’ll need it for the next question.#### Diagram Description:The diagram displays a network of six nodes labeled A, B, C, D, E, and F with weighted edges indicating the cost to traverse from one node to another. The node E is marked in red. The weights are as follows:- A to B: 10- A to C: 3- A to D: 2- B to F: 2- C to B: 4- C to D: 11- D to F: 7#### Table:| Step | N' | D(A),p(A) | D(B),p(B) | D(C),p(C) | D(D),p(D) | D(F),p(F) ||------|----|-----------|-----------|-----------|-----------|-----------|| 0 | E | * | * | * | * | * || 1 | * | * | * | * | * | 2,E || 2 | (i)| (ii) | (iii) | (iv) | (v) | * |#### Dropdown Options:- 6,F- 1,E- 8,F- 4,E- EFB- 8,D- 6,D- EFD- 9,D#### Instructions:1. Match the correct option for each position (i) through (v) based on Step 2 of Dijkstra's algorithm.2. Make sure to choose the values that complete the path calculation from node E to all other nodes as per the algorithm’s logic.After completing the table, ensure that the entries logically represent the shortest paths at step 2 in the algorithm execution.

Dijkstra's link-state algorithm is a network routing algorithm used in computer networking to find the shortest path between nodes in a network. It operates by building a complete map of the network's topology, known as a link-state database, which contains information about all nodes and their links. Using this database, Dijkstra's algorithm calculates the shortest path from a source node to all other nodes in the network by iteratively selecting the node with the smallest accumulated cost. It ensures that the shortest path is determined accurately, making it suitable for routing in networks where minimizing latency or cost is critical, such as the Internet and telecommunications networkIf a data packet is reaching from E to A and we are going to find the first router we have to find all paths from E to A. The first node of the shortest path from E will work as a first router. Here we have three paths Path 1:E-->B-->A having the cost of 13Path 2: E-->D-->A having the cost of 8Path 3: E-->D-->C--->A having the cost of 10Path 2 has the lowest cost so the first node from E to A is D.So D is the final answerStep 0: From node E the edges available are :(E, B )with cost = 10 ; (E,D)with cost = 4; (E,F) with cost =2Step 1: Choose the least cost edge in step 0, Choose node 'F' with least cost = 2Now current node N' is 'F'update the costs from E to other nodes via Fdistance(E, B) = distance(E,F) + distance(F,B) = 2+ 4 = 6 which is less than existing cost, so update D(B) with cost =6 and p(B) =FThere is no update to other nodes because there are no other edges from F to the remaining nodes. Step 2: Choose the least cost node, 'D' with cost = 4Now the current node is: 'D'update the costs from E to other nodes via 'D'd(E,A) via D = d(E,D) + d(D,A) =4+4 = 8, p(A) =DThere is no update on D(B), There is no edge from D to Bd(E,C) via D = d(E,D) + d(D,C) = 8 which is less than infinity, so update D(C)Step 3: Choose the least cost node, 'B' with cost = '6now the current node is: 'B'Update the table as we have a direct path from B to A and a direct path from B to C.For all other nodes, we already have the least cost.StepN'D(A), p(A)D(B), p(B)D(C),p(C)D(D),p(D)D(F),p(F)0Einfinity10,Einfinity4,E2,E1Finfinity6, Finfinity4,E2,E2D8, D6, F8, D4, E2,E3B3, A6, F8, D4, E2,EConclusion StepN'D(A), p(A)D(B), p(B)D(C),p(C)D(D),p(D)D(F),p(F)0Einfinity10,Einfinity4,E2,E1Finfinity6, Finfinity4,E2,E2D8, D6, F8, D4, E2,E3B3, A6, F8, D4, E2,ED is the final answer

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Computer Science

5.03-3. Dijkstra's Algorithm (3, part 3). Consider the network shown below, and Dijkstra's link-state algorithm. Here, we are interested in computing the least cost path from node E to all other nodes using Dijkstra's algorithm. Using the algorithm statement used in the textbook and its visual representation, complete the "Step 2" row in the table below showing the link state algorithm's execution by matching the table entries (i), (ii), (iii), (iv) and (v) with their values. Write down your final [correct] answer, as you'll need it for the next question. Step 0 (i) E (iii) (iv) (v) - 2 1 A 2 3 2 B 8 N' E € 10 E 2 (ii) F A D(A),p(A) D(B) [Choose ] 6,F 1,E 8,F 4,E EFB 8,D 6,D EFD 9,D [Choose ] [Choose ] [Choose ] [Choose ] [Choose ] < F D(F),p(F) 2,E

5.03-3. Dijkstra's Algorithm (3, part 3). Consider the network shown below, and Dijkstra's link-state algorithm. Here, we are interested in computing the least cost path from node E to all other nodes using Dijkstra's algorithm. Using the algorithm statement used in the textbook and its visual representation, complete the "Step 2" row in the table below showing the link state algorithm's execution by matching the table entries (i), (ii), (iii), (iv) and (v) with their values. Write down your final [correct] answer, as you'll need it for the next question. Step 0 (i) E (iii) (iv) (v) - 2 1 A 2 3 2 B 8 N' E € 10 E 2 (ii) F A D(A),p(A) D(B) [Choose ] 6,F 1,E 8,F 4,E EFB 8,D 6,D EFD 9,D [Choose ] [Choose ] [Choose ] [Choose ] [Choose ] < F D(F),p(F) 2,E

Database System Concepts

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ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

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Heuristic System

The term heuristic is derived from the Greek word heurisko, which means “I find, discover”. Heuristics can be mental shortcuts or approaches designed from previous experiences. The main aim of the heuristic approach is to find a good enough solution to solve the problem. Test and mistake, rule of thumb, or an educated estimate are all examples of heuristics. These methods are sufficient for achieving an immediate, brief aim. When a heuristic is used in practice, it works as predicted. It can, however, produce systematic errors. Trial and error is an important heuristic that may be used in a variety of situations, from cross-linking nuts and bolts to determining the values of given input variables in mathematical puzzles. Additional hypotheses, visual illustrations, simplification, and forward or backward reasoning are all common heuristics in mathematics.

Question

### Dijkstra's Algorithm (3, part 3)

Consider the network shown below and Dijkstra’s link-state algorithm. Here, we are focused on computing the least cost path from node E to all other nodes using Dijkstra’s algorithm. Using the algorithm statement and its visual representation, complete the "Step 2" row in the table below to show the algorithm’s execution by matching the table entries (i), (ii), (iii), (iv), and (v) with their values. Write down your final [correct] answer, as you’ll need it for the next question.

#### Diagram Description:

The diagram displays a network of six nodes labeled A, B, C, D, E, and F with weighted edges indicating the cost to traverse from one node to another. The node E is marked in red. The weights are as follows:
- A to B: 10
- A to C: 3
- A to D: 2
- B to F: 2
- C to B: 4
- C to D: 11
- D to F: 7

#### Table:

| Step | N' | D(A),p(A) | D(B),p(B) | D(C),p(C) | D(D),p(D) | D(F),p(F) |
|------|----|-----------|-----------|-----------|-----------|-----------|
| 0 | E | * | * | * | * | * |
| 1 | * | * | * | * | * | 2,E |
| 2 | (i)| (ii) | (iii) | (iv) | (v) | * |

#### Dropdown Options:

- 6,F
- 1,E
- 8,F
- 4,E
- EFB
- 8,D
- 6,D
- EFD
- 9,D

#### Instructions:

1. Match the correct option for each position (i) through (v) based on Step 2 of Dijkstra's algorithm.

2. Make sure to choose the values that complete the path calculation from node E to all other nodes as per the algorithm’s logic.

After completing the table, ensure that the entries logically represent the shortest paths at step 2 in the algorithm execution.

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Step 1: Defining Dijkstra's link-state algorithm

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