Exam 2 Date #
Exam 2 will be Next Thursday, April 9th
Tree Algos #
Prove that if you have a tree and add an edge the resulting graph is not a tree.
Prove that if you have a tree and remove an edge the resulting graph is not a tree.
DFS #
Look at textbook figure 6.5.
This diagram shows one DFS tree rooted at s.
- In this graph, could a back edge in one traversal be a forward edge in another?
- A cross edge?
- How about in a different graph?
- Show examples or prove it’s impossible.
MST #
Consider the following minimum spanning tree algorithm for an undirected graph with minimum weight edges:
- Replace each edge with weight w in the graph with a string of w edges with intermediate vertices.
- Do a breadth-first search.
- The first path connecting original vertices is an edge in the MST.
Prove that works, or not. If not, how can we fix it?
Shortest Paths #
The textbook says that it’s possible for a graph to have every shortest path tree use different edges from the MST. Can we show this?
All Pairs Shortest Paths #
Can we do better on all-pairs shortest paths than Floyd-Warshall in an undirected, unweighted graph?
Min Flow / Max Cut #
Can we make negative edge weights meaningful here?
Applications of Flow / Cut #
We can identify connected subgraphs using an extra source vertex and graph search.
Can we construct a flow graph to identify the number of connected components of a possibly unconnected graph?
