When reformulating a shortest path problem as a minimum cost flow problem, each link should be replaced by a pair of arcs pointing in opposite directions.

Question

Quizplus · Accepted Answer

This is because a link in a shortest path problem only allows flow in one direction, while in a minimum cost flow problem, flow can go in both directions. By replacing each link with a pair of arcs pointing in opposite directions, we are able to model the bidirectional flow that is allowed in a minimum cost flow problem. Additionally, we assign a cost to each arc, which represents the cost of sending flow in that direction.

When Reformulating a Shortest Path Problem as a Minimum Cost