1. Shortest Paths using LP: (5 points) Shortest paths can be cast as an LP using distances dv from the source s to a particular vertex v as variables.

We can compute the shortest path from s to t in a weighted directed graph by solving.

max dt

subject to

ds = 0

dv du w(u,v) for all (u,v)E

We can compute the single-source by changing the objective function to

Use linear programming to answer the questions below. Submit a copy of the LP code and output.

a) Find the distance of the shortest path from G to C in the graph below.

b) Find the distances of the shortest paths from G to all other vertices.

1. Shortest Paths using LP: (5 points) Shortest paths can be cast as an LP using distances dv from the source s to a particular vertex v as variables. We can compute the shortest path from s to t in a weighted directed graph by solving. max dt subject to dv du S w(u,v for all (u, v EE We can compute the single-source by changing the objective function to max vev. dv Use near programming to answer the questions below. Submit a copy of the LP code and output a) Find the distance of the shortest path from G to Cin the graph below b) Find the distances of the shortest paths from G to all other vertices 10 10 25