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Given the general class of graphs in Fig 2, what is the worst case time complexity of Dijkstra's algorithm on this graph (as a function of IV)? Explain your answer with proper Math. AAA Figure 2: Directed graph with negative edges

Given the general class of graphs in Fig 2, what is the worst case time complexity of Dijkstra's algorithm on this graph (as a function of IV)? Explain your answer with proper Math. AAA Figure 2: Directed graph with negative edges

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Problem 3 In tutorial 6, you saw why the original Dijkstra's algorithm doesn't work when the graph has negative weight edges and how to modify the Dijkstra's algorithm to work in case negative weight edges are present (but no negative cycle). Algorithm 1: Modified Dijkstra Result: SSSP from st dist(s) = 0; for all vertices vs do | dist(v) = ∞o end ; Insert(s, 0) - This inserts s into the priority queue along with 0. while Priority Queue is not empty do u end end extract_min() extract_min() extracts the vertex with the min dist() from the priority queue; for all edges u → v do if dist (v) dist (v) dist(u) + weight(u → v) then dist(u) + weight (u →v); if v is in the priority queue then decrease_key(v, dist(v)) - This updates the value of dist (v) in the priority queue; else | Insert(v, dist(v)); end Given the general class of graphs in Fig 2, what is the worst case time complexity of Dijkstra's algorithm on this graph (as a function of V)? Explain your answer with proper Math.
Transcribed Image Text:Problem 3 In tutorial 6, you saw why the original Dijkstra's algorithm doesn't work when the graph has negative weight edges and how to modify the Dijkstra's algorithm to work in case negative weight edges are present (but no negative cycle). Algorithm 1: Modified Dijkstra Result: SSSP from st dist(s) = 0; for all vertices vs do | dist(v) = ∞o end ; Insert(s, 0) - This inserts s into the priority queue along with 0. while Priority Queue is not empty do u end end extract_min() extract_min() extracts the vertex with the min dist() from the priority queue; for all edges u → v do if dist (v) dist (v) dist(u) + weight(u → v) then dist(u) + weight (u →v); if v is in the priority queue then decrease_key(v, dist(v)) - This updates the value of dist (v) in the priority queue; else | Insert(v, dist(v)); end Given the general class of graphs in Fig 2, what is the worst case time complexity of Dijkstra's algorithm on this graph (as a function of V)? Explain your answer with proper Math.
Given the general class of graphs in Fig 2, what is the worst case time complexity of Dijkstra's algorithm on this graph (as a function of [VI)? Explain your answer with proper Math. -16 -4.0/ Figure 2: Directed graph with negative edges
Transcribed Image Text:Given the general class of graphs in Fig 2, what is the worst case time complexity of Dijkstra's algorithm on this graph (as a function of [VI)? Explain your answer with proper Math. -16 -4.0/ Figure 2: Directed graph with negative edges
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