DIJKSTRA'S LINK STATE ALGORITHM (FOR COMPUTING LEAST COST PATHS) Consider the 6-node network shown below, with the given link costs. u 5 QUESTION 1 OF 3 5 1 X 6 W 6 Using Dijkstra's algorithm, find the least cost path from source node U to all other destinations and answer the following questions What is the shortest distance to node v and what node is its predecessor? Write your answer as Z
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- Consider the network shown below, and Dijkstra’s link-state algorithm. Here, we are interested in computing the least cost path from node E to all other nodes using Dijkstra's algorithm. Using the algorithm statement used in the textbook and its visual representation, complete the "Step 3" row in the table below showing the link state algorithm’s execution by matching the table entries (i), (ii), (iii), (iv) and (v) with their values.Example: Find the shortest path between the Node (x) and all the remaining Nodes (y, w, z, v, t, u and s) in the network shown in Figure below by Dijkstra’s Algorithm.Q-3: Write a linear programming model for the network given below which can be used to find the shortest path between nodes 1 to 7. 16 9 35 3 15 12 25 22 14 17 19 6 14 8
- Using Dijkstra’s Shortest Path Algorithm, and Figure 2(a): the network with cost between each node, fill out table 2(b): shortest distance from vertex (node) A to all other nodesUse the provided data to create the Dijkstra Shortest Weighted Path method.Precondition: S is a node in the weighted (directed or undirected) network G.Post-cond: specifies the shortest weighted route between each node of G and s, and d specifies the lengths of those paths.In a network of N nodes, how many iterations are required for Dijkstra's algorithm to completes its execution. Hint: Section 5.2.1 has the pseudo code for Dijkstra's link state algorithm that finds the shortest path from a source node to every node in the network. Professor Kurose shows the pseudo code in his video. The pseudo code in the text shows an initialization step and then a loop. How many times would the loop be executed for a network of N nodes? O N+1 times ON-1 times ON times O N² times
- Dijkstra’s algorithm computes the least-cost path from one node (the source, which we will refer to as ?u) to all other nodes in the network. Dijkstra’s algorithm is iterative and has the property that after the k-th iteration of the algorithm, the least-cost paths are known to k destination nodes, and among the least-cost paths to all destination nodes, these k paths will have the k smallest costs. Let - D(v): cost of the least-cost path from the source node to destination ?v as of this iteration of the algorithm. - p(v): previous node (neighbor of v) along the current least-cost path from the source to v. - N′: a subset of nodes; v is in N′ if the least-cost path from the source to ?v is definitely known. The centralized routing algorithm consists of an initialization step followed by a loop. The number of times the loop is executed is equal to the number of nodes in the network. Upon termination, the algorithm will have calculated the shortest paths from the source…give an example of a network with no more than 6 nodes and define all the data structure used by a distence vector and a link state algorithm. perform one iteration for both the algorithm families and show the aforementioned structires are uptadedProblem 8. The diagram below shows an instance of NETWORKFLOW that someone has started to solve using the Augmenting Path algorithm. Finish running the algorithm. Show enough work to convince me you are using the algorithm. For example, draw the residual graph at least once and list the augnenting path(s) you ue 15/18. B 15/20 15/25 0/10 5/18 T. 5/14 5/25 E 0/30 0/26
- Construct an undirected network diagram using the given set of nodes and arcs, also find the shortest path and distance from node A to node E using Dijkstra’s algorithm. Nodes {A, B, C, D, E} Arcs {(AB)=2, (AC)=3, (BC)=2, (CD)=1, (DB)=2, (DE)=1, (CE)=6}In this question, we consider the operation of the Ford-Fulkerson algorithm on the network shown overleaf: 0/16 0/12 0/8 0/4 0/8 0/5 19 0/11 174 0/13 0/14 0/2 0/11 0/10 Each edge is annotated with the current flow (initially zero) and the edge's capacity. In general, a flow of x along an edge with capacity y is shown as x/y. (a) Show the residual graph that will be created from this network with the given (empty) flow. In drawing a residual graph, to show a forward edge with capacity x and a backward edge with capacity y, annotate the original edge *;ỹ. (b) What is the bottleneck edge of the path (s.₁,vs,t) in the residual graph you have given in answer to part (a)?Q1 Consider the following graph representing a network with a, b, c, d, e and z routers andthe metric is the distance. Image attached based on the attached image please show execution of Dijkastra’s algorithm to find the shortest path from router a to all other routers. Thank you in advance!