Dijkstra's single-source shortest path algorithm makes use of a priority queue Q of vertices with an associated value on which the queue is sorted and a set 5 of processed vertices for which it has determined the shortest distance from the source vertexs. The value on which the priority queue is ordered is the shortest distance from the source vertex s to the vertex u in Q using only vertices within S O True O False

Partial Question 6 Bi-directional Dijkstra's algorithm can resolve single pair shortest path faster because: (1) It may not need to go through all of the vertices when it stops. (2) It may terminate much earlier when the forward and backward queues cannot provide any better solution. (3) It uses a different way to relax the edges in the backward Dijkstra steps. (4) It may not need to relax all of the edges in the graph. (5) Backward Dijkstra algorithm performs more efficient than the forward procedure. (2) (3) (4) (5)

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Kruskal's minimum spanning tree algorithm is executed on the following graph. F 7 B 3 5 D G 8 2 C 1 4 9 E What is the first edge that will be added to the result? What is the second edge that will be added to the result? What is the first edge that will NOT be added to the result? What is the minimum spanning tree edge weight sum? Ex: YZ Ex: 10

2. Consider the following weighted graph. A J 45 20 60 10 H K 15 15 60 30 G 10 20 25 15 10 F 30 B 15 20 5 E 10 20 D (a) Apply Dijkstra's Algorithm to the graph with A as the source/root. Draw the final graph its labeling produced by the algorithm. (I don't need to see each step!) (b) Draw the minimum distance spanning tree associated with the algorithm with A as the root. Label the vertices! (c) Apply Dijkstra's Algorithm to the graph with E as the source/root. Draw the final graph its labeling produced by the algorithm. (I don't need to see each step!) (d) Draw the minimum distance spanning tree associated with the algorithm with E as the root. Label the vertices! (e) What is the shortest weighted WALK from A to K that passes through E?

Luby’s Algorithm: 1. Input: G = (V, E)2. Output: MIS I of G3. I ← ∅4. V ← V5. while V = ∅6. assign a random number r(v) to each vertex v ∈ V7. for all v ∈ V in parallel8. if r(v) is minimum amongst all neighbors9. I ← I ∪ {v}10. V ← V \ {v ∪ N(v)}Make Implementation of this algorithm in sequential form in Python. dont copy ans from bartleby its wrong

Python code for the BFS algorithm which returns the visited vertices in visited which is copied to kth entry of dictionary comps. Each time we call the BFS algorithm, a new list is returned which is copied as a new entry to comps.

Use Dijkstra's algorithm to construct a shortest path tree starting from vertex_ that includes all vertices in the original graph. Use the format shown in the given table. After filling in the table, draw the resulting shortest path tree in the empty box. 2 6 b fringe list 2 a STEP vertices in tree next edge to add 9 9 1 d с 4 12 2 2 2 f 9 1 h 3 4 5 6 7 8

Luby’s Algorithm: 1. Input: G = (V, E)2. Output: MIS I of G3. I ← ∅4. V ← V5. while V = ∅6. assign a random number r(v) to each vertex v ∈ V7. for all v ∈ V in parallel8. if r(v) is minimum amongst all neighbors9. I ← I ∪ {v}10. V ← V \ {v ∪ N(v)}Make Implementation of this algorithm in sequential form in Python