28.2. Negative Edges: Bellman-Ford Algorithm

Try these first

1. 1.

   What does a negative edge represent in a graph?

   Hint

   Think about costs in comparison.

2. 2.

   Explain the significance of no negative cycles in using the Bellman-Ford algorithm.

   Hint

   Focus on how cycles affect path calculations.

3. 3.

   What is the primary advantage of the Bellman-Ford Algorithm over Dijkstra's?

   • Handles negative edges
   • Faster computations
   • Requires fewer iterations

   Hint

   Focus on how different edge weights are managed.

4. 4.

   True or False: The Bellman-Ford Algorithm can produce invalid results with negative cycles.

   • True
   • False

   Hint

   Think about what happens to distances in cycles.

5. 5.

   Given a directed graph with vertices having both positive and negative edges, provide a detailed step-by-step solution using the Bellman-Ford algorithm, ensuring to explain the reasoning during each iteration.

   Hint

   Focus on the relationships between vertices and their edges.

6. 6.

   Create a graph that includes a negative cycle and explain how the Bellman-Ford Algorithm behaves with that graph.

   Hint

   Consider how to signify paths that decrease indefinitely.