Suppose that CONTROL, a secret U.S. government counterintelligence agency based in Washington, D.C., has build a communication network that links n stations spread across the world using m communication channels between pairs of stations (i.e., edges).

Suppose further that the evil spy agency, KAOS, is able to eavesdrop on some number, k, of these channels and that CONTROL knows the k channels that have been compromised. Now, CONTROL has a message, M, that it wants to send from its headquarters station, s, to one of its field stations, t. The problem is that the message is super secret and should traverse a path that minimizes the number of compromised edges that occur along this path.

Explain how to model this problem as a shortest-path problem, and describe and analyze an efficient algorithm to solve it.