1. Consider the following weighted graph. F B 10 5 G 15 E 30 D 5 10 5 15 20 A (a) Apply Dijkstra's Algorithm to the graph with A as the source/root and draw the graph for EACH step of the algorithm (include the initial state!). (b) Draw the minimum distance spanning tree associated with the algorithm with A as the root. Label the vertices! (c) Suppose a new graph is formed by deleting the edge between D and E. Run Dijkstra's Algorithm on this new graph with A as the source/root. You only need to provide the final graph produced by the algorithm.

1. Consider the following weighted graph. F B 10 5 G 15 E 30 D 5 10 5 15 20 A (a) Apply Dijkstra's Algorithm to the graph with A as the source/root and draw the graph for EACH step of the algorithm (include the initial state!). (b) Draw the minimum distance spanning tree associated with the algorithm with A as the root. Label the vertices! (c) Suppose a new graph is formed by deleting the edge between D and E. Run Dijkstra's Algorithm on this new graph with A as the source/root. You only need to provide the final graph produced by the algorithm.

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

Section: Chapter Questions

Problem 1PE

See similar textbooks

Related questions

Q: 7. Consider the following graph: B A •C D (a) Write the degree of each vertex (write it next to the…

A: 7 a) Degree of vertex: Degree of a vertex is denoted by the number of the edges that are connecting…

Q: Consider the graph below. Use Prim's algorithm to find a minimal spanning tree of the graph rooted…

Q: 1. Consider the graph below. Find the betweenness of the following edges (a) AB (b) BC (c) DE F D

A: As I have read the guidelines I can provide answers to only 1 part of the questions in case of…

Q: 1. For the undirected graph in Figure 1, perform a depth-first search starting at the vertex marked…

A: We need to perform DFS on given graph. DFS algorithm: 1. Put starting vertex on top of a stack.2.…

Q: The graph below does not have an Euler path and does not have an Euler circuit.

A: a) Euler Path: A path that travels every edge of a connected graph once and only once and starts…

Q: 1) Find the minimum spanning tree of the following graph by applying Kruskal's Algorithm of the…

A: Kruskal's Algorithm :It is used to find the minimum spanning tree. It uses greedy approach.Steps…

Q: 19. Use the graph K; to answer the following questions. 6/6 9/11 3/4 6/6 3/3 3/3 2/2 8/8 1/1 b K2 a.…

A: According to the information given:- We have to identify a cycle in the graph and reduce flow in the…

Q: D I A E H F В G Suppose you run a topological sort on the shown graph starting at vertex B. Use the…

A: It takes as input a directed graph G(V,E) and produces as output set of vertices where each vertex…

Q: 1. Consider the input graph 5 1 3 7 4 2 6 where vertices are labeled with their weights. What are…

A: Here given a input graph: ========================================================== Answer 1: given…

Q: a d b a) Give the vertex set of the G. b) Give the set of edge of G. c) Find the degree of each of…

A: In this question we have been given with the graph and we have to answer for the graph theory…

Q: Recall that the degree d(u) of a node u in a graph is the number of neighbors of u. Prove the…

Q: Suppose that G is an unconnected graph that consists of 4 connected components. The first component…

A: Euler Graph: A linked graph created by Euler. If there is a closed trail that contains every edge of…

Q: An undirected weighted graph G is given below: 12 2 6 Figure 16: An undirected weighted graph has 6…

A: The Answer is

Q: Starting with the tic-tac-toe program of Figure 12.4, draw a directed acyclic graph in which every…

A: Identify Clauses: Examine the tic-tac-toe program and identify the different clauses or sections of…

Q: Suppose we have a graph as follows A) Show the order of visit for the vertices using Depth First…

A: Below are the answers of BFS and DFS:

Q: Problem 7: Let G be a graph in which the sum of vertex degrees is equal 30. (a) What is the smallest…

A: Here in this question we have given let there be a graph G with sum of its vertex degree is 30..so…

Q: The questions in this section refer to this edge-weighted graph: A 7 4 7 12 E

A: Dijkstra's algorithm is a powerful and widely-used algorithm for finding the shortest paths between…

Q: Computer Science Let V be a fixed set of n vertices. Consider a sequence of m undirected edges e1,…

A: The shortest path in a graph: A classification tree (MST) or maximum weight extending tree is a…

Q: Show the formal notation V(..) and E(..) of the graph that is described by the following adjacency…

A: Given :

Q: a) List all the bridges in this graph. Enter your answers in alphabetical order separated by commas…

Q: Consider the following undirected graph. b s (a) How many edges are there in this graph? (b) Give…

A: (a) The given graph contains the following edges: a self-loop on vertex a (a-b) (a-e) (b-c) (b-d)…

Q: Question 5: Consider the following graph. Find the shortest path from 'a' to all other vertices…

Question

1. Consider the following weighted graph.

[Graph Description]
- Vertices: A, B, C, D, E, F, G.
- Edges and Weights:
- A to B: 15
- A to D: 5
- B to D: 5
- C to D: 10
- C to A: 20
- D to E: 30
- E to F: 5
- F to G: 15
- G to E: 5

(a) **Apply Dijkstra’s Algorithm** to the graph with A as the source/root and draw the graph for EACH step of the algorithm (include the initial state!).

(b) **Draw the minimum distance spanning tree** associated with the algorithm with A as the root. Label the vertices!

(c) **Suppose a new graph is formed by deleting the edge between D and E.** Run Dijkstra’s Algorithm on this new graph with A as the source/root. You only need to provide the final graph produced by the algorithm.

(d) **Explain how you know the graph from the previous question is disconnected** using only the output of Dijkstra’s Algorithm.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.

Similar questions

Given the below graph, show the minimum spanning tree using an adjacency matrix. You may use scratch paper to draw the graph if you wish. 12 A В 2 3 E F 8 G H 10 A В D E F G A В C D E F G H |||
Q7: Run the Ford-Fulkerson algorithm on the graph assigned to you and determine the maximum flow possible between the source (s) and destination (d) as well as determine the minimum cut of edges (set of edges with the minimum sum of the edge weights) to disconnect the source and destination. Show all the work (including the use of the residual graphs in each iteration).
The following is a graph theory problem: Suppose we have a graph A = (X, Y) and a subgraph of A, which is expressed as B = (x, y). x is an element of X and y is an element of Y. A subgraph is plainly described as a graph obtained from A by removing vertices &/or edges. For every following statement determine whether it is true or false. Explain or provide counterexample. Be careful when answering the following questions to leave edges that have their endpoints in B. (i) If A is connected then B is connected (and vice versa: If B... then A) (ii) If A is simple graph then B is simple graph (and vice versa: If B... then A) (iii) If A contains a cycle then B contains a cycle (and vice versa: If B... then A) (iv) If A is a tree then B is a tree (and vice versa: If B... then A)
2. Consider the following weighted graph. A J 45 20 60 10 H K 15 15 60 30 G 10 20 25 15 10 F 30 B 15 20 5 E 10 20 D (a) Apply Dijkstra's Algorithm to the graph with A as the source/root. Draw the final graph its labeling produced by the algorithm. (I don't need to see each step!) (b) Draw the minimum distance spanning tree associated with the algorithm with A as the root. Label the vertices! (c) Apply Dijkstra's Algorithm to the graph with E as the source/root. Draw the final graph its labeling produced by the algorithm. (I don't need to see each step!) (d) Draw the minimum distance spanning tree associated with the algorithm with E as the root. Label the vertices! (e) What is the shortest weighted WALK from A to K that passes through E?
We have the following directed graph G, where the number on each edge is the cost of the edge. 1. Step through Dijkstra’s Algorithm on the graph starting from vertex s, and complete the table below to show what the arrays d and p are at each step of the algorithm. For any vertex x, d[x] stores the current shortest distance from s to x, and p[x] stores the current parent vertex of x. 2. After you complete the table, provide the returned shortest path from s to t and the cost of the path.
Consider a graph with five nodes labeled A, B, C, D, and E. Let's say we have the following edges with their weights: A to B with weight 3 A to C with weight 1 B to C with weight 2 B to D with weight 1 C to E with weight 4 D to E with weight 2 a. Find the shortest path from A to E using Dijkstra's algorithm. (Draw the finished shortest path) b. Use Prim to find the MST (Draw the finished MST) c. Use Kruskal to find the MST (Draw the finished MST) d. What's the difference between Prim and Kruskal algorithms? Do they always have the same result? Why or why not.
7. Consider the following graph: A 14 CO D 9 E C 12 10 17 b) What is the weight of the minimum spanning tree? B Apply Kruskal's algorithm to find the minimum spanning tree. Edges are sorted first by length, and in the event of a tie, by name, where the two letters are in alphabetical order. Use makeset (x), find (x), and union (x, y) to determine if there are cycles. a) Circle the edges that are part of the minimum spanning tree. AC, AD, AE, BC, BD, BE, DE c) Draw the tree that results from applying the union-find algorithm for cycle detection. When drawing the tree, put vertices with lower letters in the left subtrees so that all the vertices in a level are sorted alphabetically from left to right
Find back-edges for the following graphs starting from smallest nodes, and then find articulation vertices. (A (H) (E) (F B D A E F Please show your work step by step.
1. Consider the weighted, directed graph containing the following vertices and edges.(Weights are in the parentheses.)Vertices: {A, B, C, D} Edges: {AB(5), BC(3), CA(4), AD(2), DA(4), CB(3)}a. Starting at vertex C, determine the shortest path tree using Dijkstrab. If you were to apply Floyd-Warshall’s algorithm to this tree, would it include the shortest path tree you found using Dijkstra? Why or why not?c. Starting at vertex C, determine the minimum spanning tree using Prim.d. Would Kruskal’s algorithm always result in the same MST as Prim’s? Why or why not?
A B. D H Suppose you run the topological sort algorithm on the graph above starting at vertex C. Use the rule that when there is a choice of vertices for the algorithm to visit, it visits them in alphabetic order. Which vertex would end up first in the eventual topologically sorted order? Which would end up being second? Which would end up being third? Which would end up being fourth? Which would end up being fifth? Which would end up being sixth?
Consider the following graph. d a g b h (a) Without adding new vertices, add a single edge to the graph so that the new graph will have an Euler path. Which vertices does your new edge connect? O b and h O i and d Od and h Oh and f O a and e (b) In addition to the edge from part (a), add a second edge (using the existing vertices) so that the resulting graph will have an Euler circuit. Which vertices does your second new edge connect? O d and c O g and b O c and e O b and i O g and f
1. Consider the weighted, directed graph containing the following vertices and edges.(Weights are in the parentheses.)Vertices: {A, B, C, D} Edges: {AB(5), BC(3), CA(4), AD(2), DA(4), CB(3)}a. Starting at vertex C, determine the shortest path tree using Dijkstrab. If you were to apply Floyd-Warshall’s algorithm to this tree, would it include the shortest path tree you found using Dijkstra? Why or why not?c. Starting at vertex C, determine the minimum spanning tree using Prim.d. Would Kruskal’s algorithm always result in the same MST as Prim’s? Why or why not? Please provide graphs if possible.