Given an undirected graph G = , a vertex cover is a subset of vertices S V such that for each edge (u,v) belongs to E, either u S or v S or both. The Vertex Cover Problem is to find minimum size of the set S. Consider the following algorithm to Vertex Cover Problem: (1) Initialize the result as {} (2) Consider a set of all edges in given graph. Let the set be E’. (3) Do following while E’ is not empty ...a) Pick an arbitrary edge (u,v) from set E’ and add u and v to result ...b) Remove all edges from E which are either incident on u or v. (4) Return result. It claim that this algorithm is exact for undirected connected graphs. Is this claim True or False? Justify the answer.
Given an undirected graph G = , a vertex cover is a subset of vertices S V such that for each edge (u,v) belongs to E, either u S or v S or both. The Vertex Cover Problem is to find minimum size of the set S. Consider the following algorithm to Vertex Cover Problem: (1) Initialize the result as {} (2) Consider a set of all edges in given graph. Let the set be E’. (3) Do following while E’ is not empty ...a) Pick an arbitrary edge (u,v) from set E’ and add u and v to result ...b) Remove all edges from E which are either incident on u or v. (4) Return result. It claim that this algorithm is exact for undirected connected graphs. Is this claim True or False? Justify the answer.
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Question
Given an undirected graph G = <V,E>, a vertex cover is a subset of vertices S V such
that for each edge (u,v) belongs to E, either u S or v S or both. The Vertex Cover Problem is to
find minimum size of the set S.
Consider the following
(1) Initialize the result as {}
(2) Consider a set of all edges in given graph. Let the set be E’.
(3) Do following while E’ is not empty
...a) Pick an arbitrary edge (u,v) from set E’ and add u and v to result
...b) Remove all edges from E which are either incident on u or v.
(4) Return result.
It claim that this algorithm is exact for undirected connected graphs. Is this claim True or
False? Justify the answer.
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