Unformatted text preview: algorithm B has a running time of 2 ) 4 / ( ) ( n n aS n S + = . What is the largest integer value for a such that B is asymptotically faster than A (i.e. such that ) ( n S has an asymptotically slower growth rate than ) ( n T .) ? 4. (1 Points) Let G be an acyclic graph with n vertices, m edges, and k connected components. Show that k n m= . (Hint: use the fact that 1  ) (   ) ( = T V T E for any tree T , from the induction handout.) 5. (1 Point) (Appendix B.4 problem 3) Show that any connected graph G satisfies 1 ) ( ) (≥ G V G E . (Hint: use induction on the number of edges.)...
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 Spring '09
 AgoreBack
 Graph Theory, Recursion, Recurrence relation, Master Theorem

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