The maximum independent set (MIS) of a graph G = (V,E) is the largest set of vertices
Question:
The maximum independent set (MIS) of a graph G = (V,E) is the largest set of vertices S ⊆ V such that for any two vertices u, v ∈ S, (u, v) ∈/ E; that is, no pair of vertices in S are neighbors. We want to create a linear program to solve the MIS problem. We create an indicator variable iv for each vertex v ∈ V , and the sum of the iv should denote the size of the MIS. Consider the following linear program formulation of the MIS problem:
What’s wrong with this formulation? Give a small example graph for which the linear program does not give a reasonable answer for the size of the maximum independent set. Why doesn’t the program give a reasonable answer in this case?
Step by Step Answer:
Algorithm Design And Applications
ISBN: 9781118335918
1st Edition
Authors: Michael T. Goodrich, Roberto Tamassia