Answered: Question 2: Find a spanning tree for…

Question 2: Find a spanning tree for this graph by tracing the depth-first search and breadth-first search algorithm and using the ordering C, D, E, F, G, H, I, J, A, B, C. B A J D E C F H G I

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

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Concept explainers

Minimum Spanning Tree

A spanning tree is a sub-graph of a connected, undirected graph. It has all the vertices of a graph with the minimum possible number of edges. If a vertex is skipped, then it will not be a spanning tree. The edges of a spanning tree may or may not have weights.

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Step 1: Finding Spanning Tree with DFS and BFS:

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Step 2: Depth-First Search (DFS) Spanning Tree:

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Step 3: Breadth-First Search (BFS) Spanning Tree:

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Kruskal's minimum spanning tree algorithm is executed on the following graph. Select all edges from edgeList that belong to the minimum spanning tree. edgeList result List AD BC BE CF EF DG EG EH GH D 7 9 G 1 B 5 3 A E H 4 2 6 8 F
Apply Prim's algorithm or Kruskal's algorithm or Borvuka's algorithm to find the minimum spanning tree for the following graph. Illustrate the algorithm stepwise while applying it on the graph. |1
Design an algorithm for finding a maximum spanning tree—a spanning tree with the largest possible edge weight—of a weighted connected graph. (Look at Kruskal’s Algorithm for supplemental information)
4. Please apply Kruskal's spanning tree algorithm in the graph below and find the minimum spanning tree (MST). Edge weights are in the adjacency matrix table. (you can list the edges in MST or draw the tree below) d b a e h f The adjacency matrix for the undirected weighted graph is mentioned below: a d e g h a 4 8 4 8 11 8. 7 4 2 d 7 14 e 9. 10 f 4 14 10 2 1 6. 8. 11 1 7 7
2. Use a deep-first search to find a spanning tree of the following graph starting from vertex а. (a) Write the list of the edges of the spanning tree in the order you add them. (b) Draw the minimal spanning tree.
I A E H F В G Suppose you run a topological sort on the shown graph starting at vertex B. Use the rule that when DFS has a choice of nodes to visit, it visits them in alphabetical order. What's the first vertex in the resulting topological order? What is the second? What is the third? What is the fourth?
Apply Kruskal's algorithm to find a minimum spanning tree of the following graph. You need to do it step by step. Answer: here a 5 b () 3 1 d 4 C 2 6 e
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Use Prim's algorithms AND the Kruskal's algorithm to find the minimum spanning tree for the given weighted graph. Draw and show each step. a 4 2 3 5 3 7 e d 8. 4 4 4 h 2 i 3. 6.
1 A spanning tree for an undirected graph is a sub-graph which includes all vertices but has no cycles. There can be several spanning trees for a graph. A weighted undirected graph can have several spanning trees One of the spanning trees has smallest sum of all the weights associated with the edges. This tree is called minimum spanning tree (MST). Find the MST in the following graph using Kruskal?s Algorithm. V={a, b, c, d, e, f, g, h, i, j} and E={(a, b, 12), (a, b, 3), (a, j, 13), (b, c, 12), (b, d, 2), (b, h, 4), (b, i, 25), (c, d, 7), (c, j, 5), (e, f, 11), (e, j, 9), (f, g, 15), (f, h, 14), (g, h, 6), (h, d, 20), (h, i, 1) }. Note: Numeric value is the weight of the corresponding edge.
Kruskal's algorithm, which incorporates the union-find data structure, is as follows.algorithm Pre-cond KruskalMST (G): G is an undirected graph.post-cond: The result is a minimum spanning tree.