Give an efficient algorithm to determine if an undirected graph G JEJ, is a tree. Justify the correctness of your algorithm and its running time complexity. The input graph is given in adjacency list representation and your algorithm must have the running time in O(n + m (V, E), with n = IV and %3D m%3D (Ctrl) -

Give an efficient algorithm to determine if an undirected graph G JEJ, is a tree. Justify the correctness of your algorithm and its running time complexity. The input graph is given in adjacency list representation and your algorithm must have the running time in O(n + m (V, E), with n = IV and %3D m%3D (Ctrl) -

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: Let G = (V, E) be a directed graph. Assume that each edge ij belongs to E has a non-negative weight…

A: Floyd Warshall Algorithm : The Floyd Warshall Algorithm is for comprehending the All Pairs Shortest…

Q: Show how given a graph G in adjacency matrix representation, it is possible to use Strassen's…

A: Algorithm: Start the program. Declare the graph as adjacency matrix. Check whether the graph…

Q: We are given an undirected graph, that is connected. We're also given that each edge is associated…

A: We can use Depth first search algorithm to detect a cycle in the graph. At the same time, we have to…

Q: Find the shortest path from any vertex in S to any vertex in T given a digraph with positive edge…

A: To find the shortest path from any vertex in S to any vertex in T, we can modify Dijkstra's…

Q: An algorithm X of an undirected graph G returns, Vc. Vc is a set of vertices of G and every edge in…

A: What type (approach) of the algorithm is the pseudo-code above? The above-mentioned algorithm…

Q: Describe a linear-time algorithm for computing the strong connected component containing a given…

A: A directed path between any two vertices defines a subgraph as a strongly connected component (SCC)…

Q: Suppose you are given a connected undirected weighted graph G with a particular vertex s designated…

A: modify the graph such that all have the same weight. edges having weight 3x split them into three .…

Q: A directed graph G = (V, E) and two vertices, s and t, are supplied. Additionally, the graph's edges…

A: A directed graph can be defined in such a way that it is a graph in which the edges have a…

Q: Create an algorithm that, given a directed graph g = (v e) and a distinguished vertex s v, finds the…

A: A directed graph, also known as a digraph, is a type of graph in which the edges have a direction…

Q: Let G be an undirected edge-weighted graph with V vertices and O(V2) edges. Describe an efficient…

A: Given that, Let G be an undirected edge-weighted graph with V vertices and O(V2) edges. only allowed…

Q: For any given graph G = (V, E), give a linear time algorithm to determine whether G is a bipartite…

A: Answer:-

Q: Johnson’s algorithm with the tightest asymptotic upper bound for its worst-case running time is…

A: Johnson’s algorithm with the tightest asymptotic upper bound for its worst-case running time is…

Q: Problem 1. A walk in a directed graph G = (V, E) from a vertex s to a vertex t, is a sequence of…

A: An algorithm is a set of precise and well-defined instructions that are used to solve a problem or…

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…

Q: Given: graph G, find the smallest integer k such that the vertex set V of G contains a set A…

A: instance will be when greedy choose a path which will be good at that time but will not give…

Q: Consider an undirected graph with n nodes and m edges. The goal is to find a path between two…

A: To solve this problem, we can use binary search along with Dijkstra's algorithm. The idea is to…

Q: Implement Dijkstra's algorithm to find the shortest path between two nodes in a graph. What is the…

A: Initialize all node distances to infinity, except for the starting node which is set to 0. Create a…

Q: You are given a directed-acyclic-graph G = (V,E) with possibly negative weighted edges: (a) Give an…

A: A mathematical representation of the relationships between pairs of things is called a graph. It is…

Q: Consider the following edge-weighted graph G with 9 vertices and 16 edges: 90 Q6.1 Kruskal 0 40 50…

A: Answer: The weights of the MST edges are

Q: Suppose you are given a directed graph G on n vertices, each of which is assigned a colour. (In this…

A: Required : algorithm to find longest monochromatic directed path in the graph G. Algorithm : set…

Q: Attached is the pseudocode for Boruvka's algorithm. What is a counterexample that shows this…

A: Boruvka's algorithm is a greedy algorithm that starts with each vertex as a separate connected…

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

Give an efficient algorithm to determine if an undirected graph G = (V, E), withn =
m = JEJ. is a tree. Justify the correctness of your algorithm and its running time complexity.
The input graph is given in adjacency list representation and your algorithm must have the.
running time in O(n + m
IV| and
!!
(Ctri) -

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

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

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

Most graph algorithms that take an n×n adjacency-matrix representation as input require at least time O(n^2), but there are some exceptions. Show how to determine whether a simple directed graph G contains a universal sink, that is, a vertex with in degree n − 1 and out-degree 0, in time O(n) given an n × n adjacency matrix for G. (A vertex v has indegree k if there are precisely k edges of the form (u, v), and has outdegree k if there are precisely k edges of the form (v, u).)
Suppose you have a polynomial-time algorithm that, given a multigraph H, computes the number of spanning forests of H. Using this algorithm as a subroutine, design a polynomial-time algorithm that, given a weighted graph G, computes the number of minimum spanning trees of G.
Suppose you have a graph with 100 nodes and 500 edges and you want to find the shortest path between two nodes using Dijkstra's algorithm. What is the time complexity of this operation?
Algebraic Preis’ AlgorithmAlgorithm due to Preis provides a different way to solve the maximal weightedmatching problem in a weighted graph. The algorithm consists of the followingsteps.1. Input: A weighted graph G = (V, E, w)2. Output: A maximal weighted matching M of G3. M ← Ø4. E ← E5. V ← V6. while E = Ø7. select at random any v ∈ V8. let e ∈ E be the heaviest edge incident to v9. M ← M ∪ e10. V ← V {v}11. E ← E \ {e and all adjacent edges to e} show two ways of implementing this algorithm in Python
A directed acyclic graph (DAG) is called a lattice if it has one vertex reach-able from any other vertex (sink), and one vertex such that every other vertex can bereached from it (source). Give an efficient algorithm to determine if a given DAG is alattice. Provide justification of the correctness and analyze running time complexity ofyour algorithm. Your algorithm has to have a running time in O(|V| + |E|)
Let G be a graph with V vertices and E edges. One can implement Kruskal's Algorithm to run in O(E log V) time, and Prim's Algorithm to run in O(E + V log V) time. If G is a dense graph with an extremely large number of vertices, determine which algorithm would output the minimum-weight spanning tree more quickly. Clearly justify your answer.
Hey, Kruskal's algorithm can return different spanning trees for the input Graph G.Show that for every minimal spanning tree T of G, there is an execution of the algorithm that gives T as a result. How can i do that? Thank you in advance!
You are given a weighted, undirected graph G = (V, E) which is guaranteed to be connected. Design an algorithm which runs in O(V E + V 2 log V ) time and determines which of the edges appear in all minimum spanning trees of G. Do not write the code, give steps and methods. Explain the steps of algorithm, and the logic behind these steps in plain English.Please give total time complexity. test whether a particular edge appears in all MSTs
The Algorithm of AlgebraThe adjacency matrix A of a graph G = is used by the algebraic BFS algorithm (V, E).First, we create a vector x with all zeros except for the index of the source vertex s that we wish to use as the starting point for the algorithm; next, we create the matrix A = A+ I; last, AT x chooses all nodes that are at a distance of 1 (level 1) from the source vertex. The vertices with the fewest number of hops are obtained by multiplying the vector x by the matrix A2. As a rule, the product Ak x will produce neighbours that are at most k hops distant, and the multiplication should be done in a boolean manner as in the algorithm shown below. Algorithm for Algebraic BFS1: Input : Adjacency matrix An,n of a graph G = (V, E) connected, unweighted graph G and asource vertex s2: Output : N, visited, levels a matrix that shows level i vertices at its column i, the visitedvertices in sequence and their levels3: x[n] ← 04: x[s] ← 15: A ← A + I6: for i = 1 to n do7: N ← AT · x8:…
Let G be an undirected edge-weighted graph with V vertices and O(V2) edges. Describe an efficient algorithm to compute a minimum spanning tree that runs in O(V2) time. You are only allowed to use data structures such as arrays and priority queues. Do not use complex data structures such as Fibonacci heaps. Give a formal proof of correctness for your algorithm. An answer without any formal proof will be considered incomplete. Analyze the running time of the algorithm.
We know that when we have a graph with negative edge costs, Dijkstra’s algorithm is not guaranteed to work. (a) Does Dijkstra’s algorithm ever work when some of the edge costs are negative? Explain why or why not. (b) Find an algorithm that will always find a shortest path between two nodes, under the assumption that at most one edge in the input has a negative weight. Your algorithm should run in time O(m log n), where m is the number of edges and n is the number of nodes. That is, the runnning time should be at most a constant factor slower than Dijkstra’s algorithm. To be clear, your algorithm takes as input (i) a directed graph, G, given in adjacency list form. (ii) a weight function f, which, given two adjacent nodes, v,w, returns the weight of the edge between them. For non-adjacent nodes v,w, you may assume f(v,w) returns +1. (iii) a pair of nodes, s, t. If the input contains a negative cycle, you should find one and output it. Otherwise, if the graph contains at least one…