In network design, which problem seeks the smallest total length network that connects a given set of points by possibly adding junctions?

In network design, which problem seeks the smallest total length network that connects a given set of points by possibly adding junctions?

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

Answer: (C)

This question targets optimizing a network to connect several points with the smallest total length while allowing extra junctions. That is the Steiner Tree Problem. It lets you add junctions (Steiner points) where lines meet, and in the plane the optimal layout often uses 120-degree angles at these points to minimize total length. If no extra points were allowed, you’d get a minimum spanning tree, which is not as short in general. This differs from the traveling salesman problem, which looks for a single loop that visits every point, not a network connecting them; Braess's paradox concerns how adding roads can paradoxically worsen travel times, and desire paths describe natural, unconstrained routes rather than an optimization of a network. So the best match is the Steiner Tree Problem.

This question targets optimizing a network to connect several points with the smallest total length while allowing extra junctions. That is the Steiner Tree Problem. It lets you add junctions (Steiner points) where lines meet, and in the plane the optimal layout often uses 120-degree angles at these points to minimize total length. If no extra points were allowed, you’d get a minimum spanning tree, which is not as short in general. This differs from the traveling salesman problem, which looks for a single loop that visits every point, not a network connecting them; Braess's paradox concerns how adding roads can paradoxically worsen travel times, and desire paths describe natural, unconstrained routes rather than an optimization of a network. So the best match is the Steiner Tree Problem.