Question

Which of the following is an application of a shortest path problem?

1) Minimize total distance traveled
2) Minimize total flow through a network
3) Minimize total cost of a sequence of activities
4) Minimize total time of a sequence of activities

Answer 1

Applications of the shortest path problem include minimizing total distance traveled, total time, and total cost of a sequence of activities. It is the most efficient route considering various constraints, with the focus on displacement as the shortest path when physical distance is an important factor.

Step-by-step explanation:

The application of a shortest path problem typically involves finding the most efficient route from one point to another within a certain set of constraints. This can take various forms depending on the context:

• To minimize total distance traveled, which implies finding the shortest physical path between two points.
• To minimize the total time of a sequence of activities, where the objective could be to reduce travel time or process time within a network.
• To minimize total cost of a sequence of activities, which could include factors like fuel, tolls, labor, and materials when taking the cheapest path in terms of expenses rather than just physical distance.

Understanding the distinction between distance and displacement is crucial. Distance measures the total path traveled, while displacement is the shortest path from the starting point to the destination. In problems where reducing the physical distance is essential, such as logistics and transportation, minimizing the displacement, or the shortest path, is the key objective.