Network Algorithm

What is Dijkstra's Algorithm used for?

• Finding the longest path in a graph

• Sorting elements in an array

• Calculating the average of a list of numbers

• Finding the shortest path in a graph

Explain the main idea behind Bellman-Ford Algorithm.

• To identify the maximum flow in a network

• To determine the minimum spanning tree of a graph

• To find the longest path in a weighted graph

• To find the shortest path from a single source vertex to all other vertices in a weighted graph by iteratively relaxing edges.

How does Dijkstra's Algorithm differ from Bellman-Ford Algorithm?

• Bellman-Ford Algorithm is greedy and finds shortest paths from a single source

• Dijkstra's Algorithm can handle negative edge weights and cycles

• Dijkstra's Algorithm is greedy and finds shortest paths from a single source, while Bellman-Ford Algorithm can handle negative edge weights and cycles.

• Dijkstra's Algorithm finds longest paths from a single source

What is the significance of negative edge weights in Bellman-Ford Algorithm?

• Negative edge weights help detect negative cycles in a graph.

• Negative edge weights improve the algorithm's efficiency

• Negative edge weights are ignored in the algorithm

• Negative edge weights always lead to incorrect results

Describe the concept of network flow in Network Flow Algorithms.

• Network flow is the amount of data that can flow through a network from a source to a destination while respecting capacity constraints.

• Network flow is the number of devices connected to a network

• Network flow is the speed at which data travels through a network

• Network flow is the process of securing a network from cyber attacks

What is the purpose of augmenting paths in Network Flow Algorithms?

• To increase the flow from the source to the sink in the network.

• To decrease the flow from the source to the sink in the network.

• To reroute the flow to a different source in the network.

• To maintain the flow at a constant level in the network.

Differentiate between maximum flow and minimum cut in Network Flow Algorithms.

• Maximum flow is the minimum amount of flow that can be sent from the source to the sink, while minimum cut is the maximum capacity of edges that when removed will disconnect the source from the sink.

• Maximum flow is the maximum amount of flow that can be sent from the source to the sink, while minimum cut is the maximum amount of flow that can be sent from the source to the sink.

• Maximum flow is the maximum amount of flow that can be sent from the source to the sink, while minimum cut is the minimum capacity of edges that when removed will disconnect the source from the sink.

• Maximum flow is the maximum capacity of edges that when removed will disconnect the source from the sink, while minimum cut is the minimum amount of flow that can be sent from the source to the sink.

Explain the Ford-Fulkerson method in Network Flow Algorithms.

• The Ford-Fulkerson method is a technique used to find the maximum flow in a flow network.

• This method always guarantees the optimal solution in network flow problems

• Ford-Fulkerson method is only applicable to undirected graphs

• The Ford-Fulkerson method is used to calculate the shortest path in a network flow

What is the role of residual capacities in Network Flow Algorithms?

• Residual capacities determine the maximum flow in Network Flow Algorithms.

• Residual capacities are used to calculate the shortest path in Network Flow Algorithms.

• Residual capacities are irrelevant in Network Flow Algorithms.

• Residual capacities help determine the available capacity for additional flow on edges in Network Flow Algorithms.