Questions: Decide if the problem would most likely be solved by finding a Hamilton path, a Hamilton circuit, or a minimum spanning tree. An executive from an internet company hires a consultant to design a series of nodes throughout a new housing development. The goal is to keep the cost as low as possible while still making sure that all homes will be wired. This problem can be solved with a because the goal is to (choose one): Hamilton path, Hamilton circuit, minimum spanning tree Visit all vertices at lowest cost and end up where you started. Visit all vertices at lowest cost. Connect all vertices at lowest cost. Travel along every edge.

Decide if the problem would most likely be solved by finding a Hamilton path, a Hamilton circuit, or a minimum spanning tree.
An executive from an internet company hires a consultant to design a series of nodes throughout a new housing development. The goal is to keep the cost as low as possible while still making sure that all homes will be wired.

This problem can be solved with a because the goal is to (choose one): Hamilton path, Hamilton circuit, minimum spanning tree
Visit all vertices at lowest cost and end up where you started.
Visit all vertices at lowest cost.
Connect all vertices at lowest cost.
Travel along every edge.

Transcript text: Decide if the problem would most likely be solved by finding a Hamilton path, a Hamilton circuit, or a minimum spanning tree. An executive from an internet company hires a consultant to design a series of nodes throughout a new housing development. The goal is to keep the cost as low as possible while still making sure that all homes will be wired. This problem can be solved with a $\square$ because the goal is to (choose one): Hamilton path, Hamilton circuit, minimum spanning tree Visit all vertices at lowest cost and end up where you started. Visit all vertices at lowest cost. Connect all vertices at lowest cost. Travel along every edge.

Solution

Solution Steps

Step 1: Identify the Problem Type

The problem involves designing a series of nodes (homes) in a housing development with the goal of minimizing cost while ensuring all homes are connected. This is a classic optimization problem related to connecting all points (vertices) at the lowest possible cost.

Step 2: Determine the Appropriate Graph Theory Concept

The problem requires connecting all vertices (homes) at the lowest cost, which aligns with the concept of a minimum spanning tree. A minimum spanning tree ensures all vertices are connected with the minimum total edge weight (cost).

Step 3: Eliminate Irrelevant Options

A Hamilton path involves visiting each vertex exactly once but does not necessarily minimize cost or connect all vertices.
A Hamilton circuit is similar to a Hamilton path but requires ending at the starting vertex, which is not the primary goal here.
The problem does not involve traveling along every edge, so the last option is irrelevant.

Thus, the correct choice is a minimum spanning tree.