H3-ie514 - i if activity a i is selected then it must start...

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Homework #3 Due: March 9, 2010 1) Let G = (V;E) be an undirected graph with n vertices and m edges. Show that if every vertex has at least n/2 edges, then the graph is connected. You may assume that n is even. As a hint, think about cuts in the graph. 2) S denotes a set of n activities {a 1 , a 2 , . . . , a n }. Associated with activity a i are its start time s i and finish time f
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Unformatted text preview: i ; if activity a i is selected then it must start at s i and finish before f i . Two activities a i and a j are compatible, if s i ≥ f j or s j ≥f i ; otherwise, they are conflicting. Design an algorithm that outputs a maximal set of compatible activities. What is the running time of your algorithm? 3)-6): AMO 2.26, 2.38, 3.10, 3.44...
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