Which concept is the optimization problem of finding the shortest route that visits every point once?

Which concept is the optimization problem of finding the shortest route that visits every point once?

• A. Braess's Paradox
• B. The Steiner Tree Problem
• C. Traveling salesman problem
• D. Dead reckoning

Answer: (C)

The traveling salesman problem asks for the shortest possible route that visits every location exactly once and then returns to the starting point. It’s a classic combinatorial optimization challenge because you must choose the order of visits, and the number of possible tours grows factorially as points increase, making the true optimum hard to find for larger sets. This captures the essence of routing to minimize distance or cost, which is why it’s so central in optimization and computer science. Other concepts describe different ideas: Braess's Paradox shows how adding a road can paradoxically worsen overall travel time in a network; the Steiner Tree Problem seeks the shortest network that connects all points, possibly using extra junctions; dead reckoning is a method for estimating current position based on a known past position and movement, not about optimizing a route.

The traveling salesman problem asks for the shortest possible route that visits every location exactly once and then returns to the starting point. It’s a classic combinatorial optimization challenge because you must choose the order of visits, and the number of possible tours grows factorially as points increase, making the true optimum hard to find for larger sets. This captures the essence of routing to minimize distance or cost, which is why it’s so central in optimization and computer science. Other concepts describe different ideas: Braess's Paradox shows how adding a road can paradoxically worsen overall travel time in a network; the Steiner Tree Problem seeks the shortest network that connects all points, possibly using extra junctions; dead reckoning is a method for estimating current position based on a known past position and movement, not about optimizing a route.