Graph Algorithms and Circuit Weights

This lesson introduces the repeated nearest neighbor algorithm, an improvement over the nearest neighbor algorithm for finding Hamiltonian circuits. The video explains how to apply the algorithm from each vertex and choose the circuit with the minimal total weight. Examples are provided for starting at different vertices, and the results are compared to find the optimal Hamiltonian circuit. The lesson concludes by highlighting the effectiveness of the repeated nearest neighbor algorithm in determining the lowest cost circuit.

What is the main advantage of the Brute Force method in finding Hamiltonian circuits?

• It requires the least computational power.

• It is the easiest to understand.

• It guarantees finding the lowest cost circuit.

• It is the fastest method.

How does the Repeated Nearest Neighbor Algorithm improve upon the Nearest Neighbor Algorithm?

• By starting from multiple vertices.

• By using a different graph.

• By reducing the number of vertices.

• By increasing the edge weights.

When applying the Nearest Neighbor Algorithm, what is the first step?

• Choose the vertex with the highest weight.

• Start at a random vertex.

• Start at a chosen vertex.

• Select the vertex with the most edges.

In the application from vertex A, which vertex is visited first?

• Vertex B

• Vertex C

• Vertex D

• Vertex E

What is the total weight of the circuit starting from vertex B and visiting E, A, D, C, and back to B?

• 22

• 19

• 20

• 21

Starting from vertex C, which vertex is visited immediately after E?

• Vertex C

• Vertex D

• Vertex B

• Vertex A

What is the total weight of the circuit starting from vertex D and visiting E, C, B, A, and back to D?

• 22

• 19

• 20

• 21

When starting from vertex E, which vertex is visited after D?

• Vertex C

• Vertex B

• Vertex A

• Vertex E

How many circuits with a total weight of 19 were found using the Repeated Nearest Neighbor Algorithm?

• Two

• One

• Three

• Four

What is the main benefit of using the Repeated Nearest Neighbor Algorithm?

• It always finds the optimal circuit.

• It increases the chance of finding the optimal circuit.

• It requires fewer calculations.

• It is faster than the Brute Force method.