1. Shortest Paths using LP:

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 in C++ 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.

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