Nearest Neighbor Algorithm Concepts

This video tutorial explains how to use the nearest neighbor algorithm to find Hamiltonian circuits in a graph. It emphasizes the importance of the starting point and provides step-by-step examples starting from different vertices. The algorithm involves selecting the edge with the smallest cost from the current vertex and continuing this process until all vertices are visited, finally returning to the starting point. The video demonstrates that different starting points can lead to different circuits.

What is the primary goal of using the nearest neighbor algorithm in graph theory?

• To identify isolated vertices

• To find the shortest path between two vertices

• To find a Hamiltonian circuit

• To determine the longest path in a graph

What is a Hamiltonian circuit?

• A path that forms a loop at the starting vertex

• A path that visits the most expensive edges

• A path that visits every edge exactly once

• A path that visits every vertex exactly once and returns to the starting point

When using the nearest neighbor algorithm, what is the first step?

• Choose the edge with the highest cost

• Select any random edge

• Choose the edge with the smallest cost from the starting vertex

• Select the edge that forms a loop

In the nearest neighbor algorithm, what should you do after visiting all vertices?

• Choose a new starting point

• Visit the vertex with the highest cost

• End the circuit at the last vertex

• Return to the starting point

What is the first edge chosen when starting at vertex A?

• Edge from A to D

• Edge from A to C

• Edge from A to E

• Edge from A to B

Why is the edge from E to B not chosen after reaching vertex E?

• It is not connected to E

• It leads to a previously visited vertex

• It forms a loop

• It has the highest cost

What is the final step in the Hamiltonian circuit starting at A?

• Return to vertex B

• Return to vertex A

• Visit vertex E

• Visit vertex C

What is the cost of the edge from B to E?

• 20

• 15

• 13

• 10

Which vertex is visited last before returning to the starting point in the circuit starting at A?

• Vertex E

• Vertex C

• Vertex D

• Vertex B

What happens when the starting point is changed to vertex B?

• The same Hamiltonian circuit is found

• A different Hamiltonian circuit is found

• No Hamiltonian circuit is found

• The algorithm fails