You are given a state graph with link costs. The running time of the algorithm should be a function of the number of states in the graph and the algorithm should guarantee that the path with shortest path cost is found. Choose the most efficient search method that meets the criteria indicated above.
Question
You are given a state graph with link costs. The running time of the algorithm should be a function of the number of states in the graph and the algorithm should guarantee that the path with shortest path cost is found. Choose the most efficient search method that meets the criteria indicated above.
Solution
The most efficient search method that meets the criteria indicated above is Dijkstra's algorithm.
Here's why:
-
Dijkstra's algorithm is a graph search algorithm that solves the single-source shortest path problem for a graph with non-negative edge path costs, producing a shortest path tree.
-
This algorithm uses a priority queue to select the next closest node to visit. It starts with a source node and iteratively adds the closest node to the source node to the shortest path tree until it reaches the destination node.
-
The running time of Dijkstra's algorithm is O((V+E)logV) where V is the number of vertices (states in the graph) and E is the number of edges (links in the graph). This is because each vertex is inserted into the priority queue once and each edge is processed once.
-
Dijkstra's algorithm guarantees that the shortest path is found because it always chooses the path with the smallest total cost so far. If there were a shorter path to a node, that path would have been chosen instead.
Therefore, Dijkstra's algorithm is the most efficient search method that meets the criteria indicated above.
Similar Questions
(a) You will investigate various search algorithms for the graph in figure 1. Edges arelabeled with their costs, and heuristic values h for states are labeled next to thestates. S is the start state, and G is the goal state. For each of the following graphsearch strategies, work out the order in which states are expanded, the path returnedby graph search, the path cost, as well as the states that are not expanded. In allsearch algorithms, assume ties are broken in alphabetical order. Draw search tree foreach search strategy to illustrate your answer.Figure 1: Search graph 12 of 5(i) Depth first search [ 3 marks](ii) Breadth First search [ 3 marks](iii) Uniform cost Search [ 4 marks](iv) A* search [4 marks](v) Greedy Search [ 2 marks](b) The heuristic values for the graph in figure 2 are not correct. For which single state (S,A, B, C, D, or G) could you change the heuristic value to make everything admissibleand consistent? What range of values are possible to make this correction? [ 4marks]Figure 2: Search graph 2Question 3(a) Explain the role probability play in Artificial Intelligence. [2 marks](b) Covid-19, Maleria and Paralysis diseases cases have been reported in Makerere Uni-versity. The Ministry of Healthy has sent a team of experts to perform a diseasediagnosis to patients suspected being suffering from the diseases within Makerereand report on their rampage as soon as possible. But as they try to perform thedisease diagnostics, they discover that these diseases exhibit similar symptoms whichmakes the diagnosis process much more complicated, thus delaying the results. Inorder to reduce on the time delay in the provision of diagnostics results in the nearfuture, they have proposed using a machine learning diagnosis system and you havebeen approached to assist in the development of such systems. Using the knowledgeof Artificial intelligence and probability theory, discuss the steps you would followin developing such a system. You should clearly state the assumptions and relevantexamples for full marks. [18 marks]
_______ is not one of the step in Link state routing algorithmQuestion 46Select one:a.Discover its neighbors and learn their network addressesb.Compute the shortest path to every other routerc.Set the distance or cost metric to each of its neighboursd.Both a and ce.All of these
Which algorithm is used to find the shortest path in a graph?Question 16Select one:Bellman-Ford algorithmTopological SortFloyd-Warshall algorithmDijkstra's Algorithm
The time complexity of the Best-first search depends on..........................................a)the number of nodes in the graph.b)the branching factor of the graph.c)the depth of the solution.d)the heuristic function used.
The shortest path problem can be solved using:A. Depth-first searchB. Breadth-first searchC. Dijkstra's algorithmD. Floyd-Warshall algorithm
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.