Background: Ch. 24.1, 24.2.
Due November 20th:
- 10.1: Given a graph G=(E,V), let e be the edge 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|)).
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