Unformatted text preview: S are adjacent. For example, { c,h,u } is an independent set in the above graph. Suppose there is a weight w ( x ) (a nonnegative number) on each vertex x o± G . The maximumindependentsetproblem (MISP) is to fnd an independent set S such that w ( S ) := ∑ x ∈ S w ( x ) is maximized. The greedy algorithm ±or solving MISP works as ±ollows: We start with S = ∅ and at each iteration we add to S the next vertex x o± the largest weight ±or which S ∪ { x } is independent. Question: Does this greedy algorithm always produce an independent set o± the largest weight? You need to justi±y your conclusion. Important —– No Late Homework Will be Accepted —–...
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 Spring '08
 Lax,R
 Graph Theory, independent set, Graph Theory Homework

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