Which problem seeks the shortest network connecting given points by adding junctions?

Which problem seeks the shortest network connecting given points by adding junctions?

• A. The Steiner Tree Problem
• B. Traveling salesman problem
• C. Explore exploit problem
• D. Desire paths

Answer: (A)

Finding the shortest network that connects given points by adding junctions centers on a problem where extra connection points can be introduced to minimize total length. This is the Steiner Tree Problem: you connect all the given points (terminals) with a network that may include new junctions (Steiner points) and aim for the minimal total length. In the plane, the optimal configuration often has segments meeting at 120-degree angles at Steiner points, and adding these junctions can drastically shorten the overall network compared with simply linking the terminals directly. For three points forming a triangle, the best network may place a Steiner point inside the triangle to connect all three with shorter total length than using only the triangle’s edges. The other options describe different goals: a shortest touring route that visits every point without adding junctions; a decision-making tradeoff between exploring and exploiting; and observed pedestrian shortcuts, none of which focus on constructing a minimal connecting network with extra nodes.

Finding the shortest network that connects given points by adding junctions centers on a problem where extra connection points can be introduced to minimize total length. This is the Steiner Tree Problem: you connect all the given points (terminals) with a network that may include new junctions (Steiner points) and aim for the minimal total length. In the plane, the optimal configuration often has segments meeting at 120-degree angles at Steiner points, and adding these junctions can drastically shorten the overall network compared with simply linking the terminals directly. For three points forming a triangle, the best network may place a Steiner point inside the triangle to connect all three with shorter total length than using only the triangle’s edges. The other options describe different goals: a shortest touring route that visits every point without adding junctions; a decision-making tradeoff between exploring and exploiting; and observed pedestrian shortcuts, none of which focus on constructing a minimal connecting network with extra nodes.