5.2-2. Dijkstra’s link-state routing algorithm. Consider Dijkstra’s link-state routing algorithm that is computing a least-cost path from node a to other nodes b, c, d, e, f. Which of the following statements is true. (Refer to Section 5.2 in the text for notation.)Group of answer choicesSuppose nodes b, c, and d are in the set N’. These nodes will remain in N’ for the rest of the algorithm, since the least-cost paths from a to b, c, and d are known.The values computed in the vector D(v), the currently known least cost of a path from a to any node v, will always decrease following an iteration.Following the initialization step, if nodes b and c are directly connected to a, then the least cost path to b and c will never change from this initial cost.The values computed in the vector D(v), the currently known least cost of a path from a to any node v, will never increase following an iteration.In the initialization step, the initial cost from a to each of these destinations is initialized to either the cost of a link directly connecting a to a direct neighbor, or infinity otherwise.
Question
5.2-2. Dijkstra’s link-state routing algorithm. Consider Dijkstra’s link-state routing algorithm that is computing a least-cost path from node a to other nodes b, c, d, e, f. Which of the following statements is true. (Refer to Section 5.2 in the text for notation.)Group of answer choicesSuppose nodes b, c, and d are in the set N’. These nodes will remain in N’ for the rest of the algorithm, since the least-cost paths from a to b, c, and d are known.The values computed in the vector D(v), the currently known least cost of a path from a to any node v, will always decrease following an iteration.Following the initialization step, if nodes b and c are directly connected to a, then the least cost path to b and c will never change from this initial cost.The values computed in the vector D(v), the currently known least cost of a path from a to any node v, will never increase following an iteration.In the initialization step, the initial cost from a to each of these destinations is initialized to either the cost of a link directly connecting a to a direct neighbor, or infinity otherwise.
Solution
The statement that is true is: "In the initialization step, the initial cost from a to each of these destinations is initialized to either the cost of a link directly connecting a to a direct neighbor, or infinity otherwise."
Explanation:
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The first statement is not necessarily true. Nodes b, c, and d will remain in N’ only if they are indeed the nodes with the least-cost paths from a. If there is a node e with a lower cost path from a, it will be added to N’ before b, c, or d.
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The second statement is not always true. The values in D(v) can increase if a shorter path is found.
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The third statement is not always true. If a shorter path to b or c is found that does not directly connect to a, the least cost path to b or c will change.
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The fourth statement is not always true. The values in D(v) can increase if a shorter path is found.
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The fifth statement is true. In the initialization step, the initial cost from a to each of these destinations is indeed initialized to either the cost of a link directly connecting a to a direct neighbor, or infinity if there is no direct link. This is the basis of Dijkstra’s algorithm.
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