Construct an example of a graph on n vertices such that running this greedy algorithm on the vertices in one order yields an independent set of size 1, and processing the vertices in a different order yields an independent set of size n−1, which is maximal. Consider the following greedy algorithm for generating maximal independent sets: starting with an empty set I,process the vertices in V one at a time, adding v to I is v is not connected to any vertex already in I. Consider an undirected graph G = (V, E). An independent set is a subset I CV such that for any vertices i, j E I,there is no edge between i and j in E. A set i is a maximal independent set if no additional vertices of V can beadded to I without violating its independence. Note, however, that a maximal independent sent is not necessarilythe largest independent set in G. Let a(G) denote the size of the largest maximal independent set in G.

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Answered: Consider the following greedy algorithm…

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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Construct an example of a graph on n vertices such that running this greedy algorithm on the vertices in one order yields an independent set of size 1, and processing the vertices in a different order yields an independent set of size n−1, which is maximal.

Consider the following greedy algorithm for generating maximal independent sets: starting with an empty set I,
process the vertices in V one at a time, adding v to I is v is not connected to any vertex already in I.

Consider an undirected graph G = (V, E). An independent set is a subset I CV such that for any vertices i, j E I,
there is no edge between i and j in E. A set i is a maximal independent set if no additional vertices of V can be
added to I without violating its independence. Note, however, that a maximal independent sent is not necessarily
the largest independent set in G. Let a(G) denote the size of the largest maximal independent set in G.

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