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(a) A cut-edge of a graph G = (V,E) is an edge whose removal paritions the graph into two or more connected components (note that some of these components can be single vertex). Give a O(|V+ E|) time algorithm to find all the cut-edges of G. Give a clear description of your slgorithm and the pseudocode and argue the running time bound. (Hint: Again this is a modification of the algorithm to find cut-vertices. What is the condition for an edge to be a cut-edge? Can it lie on a simple cycle of G?) (b) Run your algorithm on the undirected graph given in Figure 2. Show the main steps and Output the cut edges of the graph.

(a) A cut-edge of a graph G = (V,E) is an edge whose removal paritions the graph into two or more connected components (note that some of these components can be single vertex). Give a O(|V+ E|) time algorithm to find all the cut-edges of G. Give a clear description of your slgorithm and the pseudocode and argue the running time bound. (Hint: Again this is a modification of the algorithm to find cut-vertices. What is the condition for an edge to be a cut-edge? Can it lie on a simple cycle of G?) (b) Run your algorithm on the undirected graph given in Figure 2. Show the main steps and Output the cut edges of the graph.

Database System Concepts
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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Exercise 11.5 (a) A cut-edge of a graph G = (V, E) is an edge whose removal paritions the graph into two or more connected components (note that some of these components can be single vertex). Give a O(|V]+ E) time algorithm to find all the cut-edges of G. Give a clear description of your algorithm and the pseudocode and argue the running time bound. (Hint: Again this is a modification of the algorithm to find cut-vertices. What is the condition for an edge to be a cut-edge? Can it lie on a simple cycle of G?) %3D (b) Run your algorithm on the undirected graph given in Figure 2. Show the main steps and output the cut edges of the graph. 1 3 7 3 DFS Tree Figure 2
Transcribed Image Text:Exercise 11.5 (a) A cut-edge of a graph G = (V, E) is an edge whose removal paritions the graph into two or more connected components (note that some of these components can be single vertex). Give a O(|V]+ E) time algorithm to find all the cut-edges of G. Give a clear description of your algorithm and the pseudocode and argue the running time bound. (Hint: Again this is a modification of the algorithm to find cut-vertices. What is the condition for an edge to be a cut-edge? Can it lie on a simple cycle of G?) %3D (b) Run your algorithm on the undirected graph given in Figure 2. Show the main steps and output the cut edges of the graph. 1 3 7 3 DFS Tree Figure 2
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