Homework 10

Background: Ch. 24.1, 24.2.

Due November 25th:

• 10.1: Given a graph G=(E,V), let e be the second smallest edge in G according to the weight function w. Argue that there is an MST containing e.
• 10.2: Argue that the choice of initial node r in PRIM-MST effects the final tree returned by constructing an example in which two different choices of r lead to two different trees. Argue that, ultimately, the choice is immaterial in that it doesn't effect the cost of the final tree.
• 10.3: Give tight asymptotic ranges of the number of edges for which a Fibonacci-heap-based implementation of Prim's algorithm is asymptotically better than the heap or simple list-based data structure. Your answer should have the form , |E|=o(g(|V|)).
• 10.4: CLR Exercise 24.1-8 (pg. 503). Extra credit.
• 10.5: CLR Exercise 24.2-6 (pg. 510). Hint: You may use the result of the extra credit problem, even if you don't solve it yourself.