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Unformatted text preview: 3colored. Use the graph coloring reduction operators in the paper on G’. That is, show a sequence of reductions on G’ that reduce it to a small graph that can be easily 3colored. Show the resulting 3coloring of the entire graph G’. v 1 v 2 v 3 v 4 v 5 v 6 v 7 v 8 G UML CS Algorithms 91.503 (section 201) Spring, 2011 2 3 . (20 points) Show that the following problem is in NP (source: Garey & Johnson): INSTANCE : An n x n matrix M of 0’s and 1’s, and a positive integer K . QUESTION : Is there a collection of K or fewer twodimensional axisaligned rectangles that covers precisely those entries in M that are 1’s? Notes : 1. Rectangles may overlap each other. 2. A matrix entry is equal to 1 if and only if that entry is inside at least one of the rectangles. Provide pseudocode as part of your answer. 4 . (40 points) Problem 344 (a) and (b) on p. 1104 of our textbook....
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 Spring '11
 Staff
 Algorithms, Computational complexity theory, NPcomplete, UML CS, Reduction Operators, Gary & Johnson, twodimensional axisaligned rectangles

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