Question textRecall Dijkstra's algorithm. We provide it below, as given in the course notes. [table] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | function DIJKSTRA(G = (V, E), s) dist[1..n] = ∞ pred[1..n] = 0 dist[s] = 0 Q = priority_queue(V[1..n], key(v) = dist[v]) while Q is not empty do u = Q.pop_min() for each edge (u, v) that goes from u to a node v still in the queue do // Priority queue keys must be updated if relax improves a distance estimate! RELAX((u, v)) return dist[1..n], pred[1..n] function RELAX((u, v)) if dist[v] > dist[u] + w (u, v) then dist[v] = dist[u] + w (u, v) pred[v] = u [/table] Given the undirected graph below, in which order will Dijkstra's algorithm pop vertices out of its queue with ? 2 4 1 3 10 2 5 8 4 7 6 1 a b c d e f g List the vertex indices in the order they are popped out of the queue. In case multiple vertices have the minimum key in the priority queue, break this tie by using the smallest index. Answer 1 Question 2[input] → Answer 2 Question 2[input] → Answer 3 Question 2[input] → Answer 4 Question 2[input] → Answer 5 Question 2[input] → Answer 6 Question 2[input] → Answer 7 Question 2[input]多项填空题

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Question textApply Dijkstra's algorithm to find the shortest path from node 1 to all other nodes in the following directed graph. The numbers on the arcs represent costs , with data provided again below for completeness. Node 1: Node 2: Node 3: Node 4: Node 5: Node 6: Node 7: Node 8: Enter the shortest distance from node 1 to each node: Node 3: Answer 1 Question 3[input] predecessor = Answer 2 Question 3[input] Node 4: Answer 3 Question 3[input] Node 5: Answer 4 Question 3[input] If the problem of finding a shortest path from node 1 to node 3 was solved as a linear program with arc flow variables , then:The reduced cost of would be Answer 5 Question 3[input] If is the optimal value of the dual variables for the flow conservation constraints, then Answer 6 Question 3[input]
Dijkstra's Link State Algorithm Consider the incomplete 6-node network shown below, with given link costs; where links x and y are unknown Consider the completed table below, which calculates the shortest distance to all nodes from U: Nodes d, (p) d, (p) d, (p) d, (p) d, (p) U V W X Y Z shortest distance from node U 0 4, X 3, U 1, U 5, X 6, W For link x (link from node X, to node Y) , what is the cost associated with this link? [Fill in the blank] For link y (link from node U to node W) , what is the cost associated with this link?[Fill in the blank]
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