Given the following network configuration (A,B... stand for node name, 1,2.. stand for the length of the link), please apply Dijkstra's algorithm to calculate the shortest path from A to all the other nodes and answer following questions.

Shouldn't the number of paths from D to E be C(6,2) and from E to C be C(4,2)?

5.04-4. Bellman Ford Algorithm - a change in DV (1, part 4). Consider the network below, and suppose that at t=0, the link between nodes b and c goes down. And so at t=0, node b recomputes its distance vector (DV) and sends out its new DV (as needed). At t=1 this new DV is received at b's neighbors, who then perform their calculation and send out their new DVs (as needed); these new DVs arrive at their neighbors at t=2, and so on. What is the last time in this network at which a DV calculation will take place as a result of the link change at t=0? U O O o 1 1 3 2 at t=0 the link (with a cost of 1) between nodes b and c goes down A 8 1 6 compute 1 1 1 1 an essentially infinite amount of time; this is the count-to-infinity problem 1 Second

"Dijkstra's single-source shortest path algorithm returns a results grid that contains the lengths of the shortest paths from a given vertex [the source vertex] to the other vertices reachable from it. Develop a pseudocode algorithm that uses the results grid to build and return the actual [shortest] path, as a list of vertices, from the source vertex to a given [target] vertex. (Hint: This algorithm starts with a given vertex [the target vertex] in the grid's first column and gathers ancestor [parent] vertices, until the source vertex is reached.)" *For your algorithm, assume that grid is the name of the results grid produced by Dijkstra's single-source shortest path algorithm. *Each vertex is identified by its label/name, which is in column 1 of grid. *As the first step of your algorithm, find the name of the source vertex. *Next, get the name of the target vertex from the user. Pseudocode should avoid details through broad-stroke statements. However, it must give enough information…

Consider the network below: G H Create a spanning tree for this network using node A as the root. Show the steps of the algorithm as you do this. The order of the nodes is alphabetical.

5.04-3. Bellman Ford Algorithm - a change in DV (1, part 3).  Consider the network below, and suppose that at t=0, the link between nodes g and h goes down. And so at t=0, nodes g and h recompute their DVs.  Following this recomputation, to which nodes will h send its new distance vector?  (Note: to answer this question, you’ll need to know some of the DV entries at g and h at t=0, but hopefully they’ll be obvious by inspection).

Estimate the biggest graph with E = 10V that your computer and programming system could manage in 10 seconds if you used Dijkstra's technique to compute all of its shortest routes.

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Mark Zuckerberg, the CEO of Facebook, has hired you to lead the Facebook Algorithms Group. He has asked you to use various graph algorithms to analyze the world's largest social network. The Facebook Graph has 2.8 billion vertices, with each vertex being a Facebook user. Two vertices are connected provided those two users are "friends". The first decision you need to make is how you want to model the Facebook graph. Determine whether you should use an adjacency-list representation or an adjacency-matrix representation.

Create an algorithm for the Dijkstra Shortest Weighted Path based on the provided data.G is a weighted (directed or undirected) network, and s is a node in it.post-cond: specifies the shortest weighted route from s to each node of G, and d the lengths of those paths.