Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Question
Chapter 22, Problem 2P
(a)
Program Plan Intro
To show that the graph Gp is an articulation point if it contains at least two children.
(b)
Program Plan Intro
To show that vertex v belongs to V is an articulation point of graph that contains child s having no back edge.
(c)
Program Plan Intro
To evaluate v .low for every vertices of the graph G in O ( E ) time.
(d)
Program Plan Intro
To compute all possible articulation points in O ( E ) time.
(e)
Program Plan Intro
To show that an edge of the graph G is a bridge if it does not contains any simple cycle.
(f)
Program Plan Intro
To configure all possible bridges of the graph G in O ( E ) time.
(g)
Program Plan Intro
To show that the graph Gbi -connected components can be partition the non-bridge edges of the graph G .
(h)
Program Plan Intro
To show that in the graph G with the edge eand e’ such that e .bcc = e’ .bcc, only possible if an edge e and e’ contains similar bi-connected component.
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Q2
a
Let G be a graph. We say that a set of vertices C form a vertex cover if every edge of G is
incident to at least one vertex in C. We say that a set of vertices I form an independent set if
no edge in G connects two vertices from I.
For example, if G is the graph above, C = [b, d, e, f, g, h, j] is a vertex cover since each of
the 20 edges in the graph has at least one endpoint in C, and I = [a, c, i, k] is an
independent set because none of these edges appear in the graph: ac, ai, ak, ci, ck, ik.
In the example above, notice that each vertex belongs to the vertex cover C or the independent
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In the above graph, clearly explain why the maximum size of an independent set is 5. In other
words, carefully explain why there does not exist an independent set with 6 or more vertices.
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A directed graph is said to be strongly connected if every vertex is reachable from every other vertex; i.e., for every pair of vertices u, v, there is a directed path from u to v and a directed path from v to u.
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Assignment on Graph
A social graph contains all the friendship relations (edges) among a group of n people
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graph[i][i] - is always true (1)
graph[i][j] is true if i and j are friends and false (0) if they are enemies.
• In the constructor, initialize all entries to false (0) and all graph[i][i] to true (1)
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Chapter 22 Solutions
Introduction to Algorithms
Ch. 22.1 - Prob. 1ECh. 22.1 - Prob. 2ECh. 22.1 - Prob. 3ECh. 22.1 - Prob. 4ECh. 22.1 - Prob. 5ECh. 22.1 - Prob. 6ECh. 22.1 - Prob. 7ECh. 22.1 - Prob. 8ECh. 22.2 - Prob. 1ECh. 22.2 - Prob. 2E
Ch. 22.2 - Prob. 3ECh. 22.2 - Prob. 4ECh. 22.2 - Prob. 5ECh. 22.2 - Prob. 6ECh. 22.2 - Prob. 7ECh. 22.2 - Prob. 8ECh. 22.2 - Prob. 9ECh. 22.3 - Prob. 1ECh. 22.3 - Prob. 2ECh. 22.3 - Prob. 3ECh. 22.3 - Prob. 4ECh. 22.3 - Prob. 5ECh. 22.3 - Prob. 6ECh. 22.3 - Prob. 7ECh. 22.3 - Prob. 8ECh. 22.3 - Prob. 9ECh. 22.3 - Prob. 10ECh. 22.3 - Prob. 11ECh. 22.3 - Prob. 12ECh. 22.3 - Prob. 13ECh. 22.4 - Prob. 1ECh. 22.4 - Prob. 2ECh. 22.4 - Prob. 3ECh. 22.4 - Prob. 4ECh. 22.4 - Prob. 5ECh. 22.5 - Prob. 1ECh. 22.5 - Prob. 2ECh. 22.5 - Prob. 3ECh. 22.5 - Prob. 4ECh. 22.5 - Prob. 5ECh. 22.5 - Prob. 6ECh. 22.5 - Prob. 7ECh. 22 - Prob. 1PCh. 22 - Prob. 2PCh. 22 - Prob. 3PCh. 22 - Prob. 4P
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