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Unformatted text preview: A graph problem: Maximal Independent Set A graph problem: Maximal Independent Set 1 8 7 6 5 4 3 2 Graph with vertices V = {1,2,,n} A set S of vertices is independent if no two vertices in S are neighbors. An independent set S is maximal if it is impossible to add another vertex and stay independent An independent set S is maximum if no other independent set has more vertices Finding a maximum independent set is intractably difficult (NPhard) Finding a maximal independent set is easy, at least on one processor. The set of red vertices S = {4, 5} is independent and is maximal but not maximum Sequential Maximal Independent Set Algorithm Sequential Maximal Independent Set Algorithm 1 8 7 6 5 4 3 2 1. S = empty set; 2. for vertex v = 1 to n { 3. if (v has no neighbor in S) { 4. add v to S 5. } 6. } S = { } Sequential Maximal Independent Set Algorithm Sequential Maximal Independent Set Algorithm 1 8 7 6 5 4 3 2 1. S = empty set; 2. for vertex v = 1 to n { 3. if (v has no neighbor in S) { 4. add v to S 5. } 6. } S = { 1 } Sequential Maximal Independent Set Algorithm...
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 Fall '11
 GILBERT

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