Question: Given a graph G = ( V , E ) , a set of vertices D subseteq V is an independent set if there

Given a graph G

= (

,

),

a set of vertices D

\

subseteq V is an independent set if there do not exist i

,

\

in D with ij

\

in E

.

Given a graph G

= (

,

)

with a function w: V

\

rightarrow

\

mathbb

{

}

that assigns a weight to each vertex, the maximum weight independent set problem consists of finding an independent set with the maximum total weight. The decision version of this problem is an NP

-

complete problem.

)

Propose a greedy algorithm for this problem. What is the computational complexity of the proposed algorithm?

)

Propose a local search algorithm for this problem.

)

Is the operator on which the local search algorithm proposed in the previous point is based connected?

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