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2 cards from this section. Quick, good the night before a test.
Define the All-pairs Shortest Paths problem.
What does 'all-pairs' refer to?
What does the Floyd-Warshall algorithm compute?
Recall the algorithm's purpose.
What does the All-pairs Shortest Paths problem focus on?
Think about what 'all-pairs' signifies.
Is it true that the Bellman-Ford algorithm is applicable for finding all pairs shortest paths?
Consider how Bellman-Ford works and its extensions.
In a directed graph defined by the following edges with their weights: (1, 2) = 10, (1, 3) = 5, (2, 3) = 2, (3, 1) = 6, apply the Floyd-Warshall algorithm step-by-step to find the distance matrix for all pairs of vertices.
Start with the initial weights and iteratively consider each vertex as an intermediate step.
Analyze the impact of introducing a negative cycle in a graph, such as adding an edge with a weight of -5 between two already connected vertices, in relation to calculating the shortest paths.
Reflect on paths you've calculated before and consider how negative totals would affect them.
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