Let G = (V, E) be an undirected and connected graph, where each edge (u, v) E E has a weight wt(u, v) > 0. Moreover, assume that all weights are equal. (a) G. The running time of your algorithm must be faster than the running time of Kruskal's algorithm. Design an algorithm to compute a minimum spanning tree (MST) of You must describe your algorithm in plain English (no pseudocode). You must write the running time of your algorithm and explain why you get this running time. (b) In at most 50 words, explain why your algorithm is correct.

Let G = (V, E) be an undirected and connected graph, where each edge (u, v) E E has a weight wt(u, v) > 0. Moreover, assume that all weights are equal. (a) G. The running time of your algorithm must be faster than the running time of Kruskal's algorithm. Design an algorithm to compute a minimum spanning tree (MST) of You must describe your algorithm in plain English (no pseudocode). You must write the running time of your algorithm and explain why you get this running time. (b) In at most 50 words, explain why your algorithm is correct.

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: You are given a graph G = (V, E) with positive edge weights, and a minimum spanning tree T = (V, E')…

A: The problem involves updating a minimum spanning tree (MST) in a graph when the weight of an edge is…

Q: I am struggling to draw a spanning tree using a depth-first when the following graph has a vertex A…

A: To get spanning tree using DFS follow the following steps :1. Start at a chosen vertex (let's say we…

Q: Please help me with this algorithm. The algorithm should be in psuedocode format. Thank you.…

A: Answer : Algorithm ConstructTPrime(G, (u,v)) Input: Graph G = (V, E) and edge (u,v) // Add…

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

Q: Use Prim's algorithms AND the Kruskal's algorithm to find the minimum spanning tree for the given…

A: below is the minimal spanning tree using given algorithms

Q: a. Using depth-first search. b. Using breadth-first search.

A: This is very simple. Solution a) DFS Path for spanning tree: abcdfejghiklmnopqrst Note: It can…

Q: a) Given a depth-first search tree T, the set of edges in T are referred to as "tree edges" while…

A: #include<stdio.h>void DFS(int);int G[10][10],visited[10],num; //num is no of vertices and…

Q: Let A, B, C, D be the vertices of a square with side length 100. If we want to create a…

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

Q: A spanning tree for an undirected graph is a sub-graph which includes all vertices but has no…

A: KRUSKAL'S ALGORITHM: Kruskal algorithm is an algorithm which is used to get a minimum spanning tree…

Q: it step by step. Answer: here a 5 b 6 3 1 d 4 2 6

A: Spanning Tree : - A spanning tree for a graph is a subgraph that includes every vertex of the…

Q: Write algorithm DijkstraShortestWeightedPath(G, s) pre-cond: G is a weighted (directed or…

A: given data: pre-cond: G is a weighted (directed or undirected) graph, and s is one of its nodes.…

Q: Consider the graph below. Use Dijkstra's algorithm to find the shortest path from vertex 0 to vertex…

Q: An undirected weighted graph G is given below: 11 3 1 -4.1 2 .2 3. b. a (a) Use Prim's algorithm to…

A: solution of the given question is:-

Q: Let A, B, C, D be the vertices of a square with side length 100. If we want to create a…

A: The Answer is

Q: Write algorithm LargestShortestWeight(G, s,t) pre-cond: G is a weighted directed (augmenting)…

A: given data: pre-cond: G is a weighted directed (augmenting) graph. s is the source node.t is the…

Q: Throughout, a graph is given as input as an adjacency list. That is, G is a dictionary where the…

A: Pseudocode is a way of describing an algorithm in a human-friendly format that doesn't have to…

Q: Problem 4. Consider the following undirected graph in which the number on each edge indicates its…

A: In given problem 4: We have to find out the minimum spanning tree using Prim's algorithm. We have to…

Q: a) Draw the connected subgraph of the given graph above which contains only four nodes ACGB and is…

A: In questions with many questions we must do the first one.

Q: ights are distinct. Is th

A: The statement is true.

Q: Consider the following weighted undirected graph. 9 A 8. 10 11 3 14 F 16 15 G H 12 13 We would like…

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: Assume you have been given a graph with 1 minimum spanning tree and no repeated edge weights. Using…

A: Boruvka's algorithm is a popular graph algorithm used to find the minimum spanning tree of a given…

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.

Question

Let G = (V, E) be an undirected and connected graph, where each edge
(u, v) E E has a weight wt(u, v) > 0. Moreover, assume that all weights are equal.
(a)
G. The running time of your algorithm must be faster than the running time of
Kruskal's algorithm.
Design an algorithm to compute a minimum spanning tree (MST) of
You must describe your algorithm in plain English (no pseudocode). You must
write the running time of your algorithm and explain why you get this running
time.
(b)
In at most 50 words, explain why your algorithm is correct.

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 6 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 |||
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
Given an undirected, weighted graph G(V, E) with n vertices and m edges, design an (O(m + n)) algorithm to compute a graph G1 (V, E1 ) on the same set of vertices, where E1 subset of E and E1 contains the k edges with the smallest edge weights , where k < m.
Consider the following weighted undirected graph. 9 A В 8. 10 11 14 F 5 16 15 G H 12 13 We would like to run the Prim's algorithm on this graph using A as initial vertex. List the edges appearing in the Minimum Spanning Tree (MST) in the order they are added to the MST.
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
Let G be a graph, where each edge has a weight. A spanning tree is a set of edges that connects all the vertices together, so that there exists a path between any pair of vertices in the graph. A minimum-weight spanning tree is a spanning tree whose sum of edge weights is as small as possible. Last week we saw how Kruskal's Algorithm can be applied to any graph to generate a minimum-weight spanning tree. In this question, you will apply Prim's Algorithm on the graph below. You must start with vertex A. H 4 4 1 3 J 2 C 10 4 8 B 9 F 18 8 There are nine edges in the spanning tree produced by Prim's Algorithm, including AB, BC, and IJ. Determine the exact order in which these nine edges are added to form the minimum-weight spanning tree. 3.
Design an algorithm to find the maximum spanning tree of any graph with a run time of O(m log m).
Given the following graph, A C 3 1 E 4 В F 7 D 5 What is the next edge and vertex(s) to be included in the solution if a. we are using Prim's algorithm to find a minimum spanning tree and we have started with vertex E? Edge: Vertex(s): What is the next edge and vertex(s) to be included in the solution if b. we are using Kruskal's algorithm to find a minimum spanning tree Edge: Vertex(s): What is the next edge and vertex(s) to be included in the solution if c. we are using Dijkstra's shortest path algorithm to find shortest paths and we have started with vertex E, with C and F already included in the shortest path tree? Edge: Vertex(s):
Write algorithm ShortestPath (G, s) pre-cond: G is a (directed or undirected) graph, and s is one of its nodes. post-cond: π specifies a shortest path from s to each node of G, and d specifiestheir lengths.
1. For the graph in Figure 12.20, use Kruskal's algorithm ("avoid cycles") to find a minimum weight spanning tree. Your answer should include a complete list of the edges, indicating which edges you take for your tree and which (if any) you reject in the course of running the algorithm. 16 20 b/47 94 14 8 8 d 5 22 12 12 13 10 8 15 16 15 i 16 8 h Figure 12.20. Find a minimum weight spanning tree 8. LO
An undirected weighted graph G is given below: 11 3 f 1 -4.1 2 .2 -1 .7 3 a .5 4 (a) Use Prim's algorithm to compute the minimum spanning tree for the weighted graph. Start the algorithm at vertex a. Show the order in which the edges are added to the tree. (b) Now suppose that the weight of edge {e,f} is decreased from 7 to -3. Is there a way to find the minimum spanning tree of the altered graph without running Prim's algorithm from scratch?
Let G = (V, E) be an undirected graph and each edge e ∈ E is associated with a positive weight ℓ(e).For simplicity we assume weights are distinct. Is the following statement true or false? Let T be a minimum spanning tree for the graph with the original weight. Suppose we replace eachedge weight ℓ(e) with ℓ(e)^2, then T is still a minimum spanning tree.