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Uninformed Search TechniquesLecture-08

Hema Kashyap

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Uninformed Search Breadth First Search Uniform Cost Search Depth First Search Depth Limited Search Iterative deepening Depth First Search Bidirectional Search

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Breadth First Search

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ConceptStep 1: Traverse the root nodeStep 2: Traverse all neighbours of root node.Step 3: Traverse all neighbours of neighbours of the root node.Step 4: This process will continue until we are getting the goal node.

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Step 8: G is selected for expansion. It is found to be a goal node. So the algorithm returns the path A C G by following the parent pointers of the node corresponding to G. The algorithm terminates.

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Properties of BFS• Complete. • The algorithm is optimal (i.e., admissible) if all operators have the same

cost. Otherwise, breadth first search finds a solution with the shortest path length.

• The algorithm has exponential time and space complexity. Suppose the search tree can be modelled as a b-ary tree as shown in Figure 3. Then the time and space complexity of the algorithm is O(bd) where d is the depth of the solution and b is the branching factor (i.e., number of children) at each node.

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Advantages

• In this procedure at any way it will find the goal.

• It does not follow a single unfruitful path for a long time.

• It finds the minimal solution in case of multiple paths.

Disadvantages

• BFS consumes large memory space.

• Its time complexity is more.• It has long pathways, when all

paths to a destination are on approximately the same search depth.

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Depth First Search

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ConceptStep 1: Traverse the root node.Step 2: Traverse any neighbour of the root node.Step 3: Traverse any neighbour of neighbour of the root node.Step 4: This process will continue until we are getting the goal node.

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Step 4: Node D is removed from fringe. C and F are pushed in front of fringe

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Step 6: Node G is expanded and found to be a goal node. The solution path A-B-D-C-G is returned and the algorithm terminates.

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Properties of DFS• The algorithm takes exponential time. If N is the maximum depth of a

node in the search space, in the worst case the algorithm will take time O(bd). However the space taken is linear in the depth of the search tree, O(bN).

• Note that the time taken by the algorithm is related to the maximum depth of the search tree. If the search tree has infinite depth, the algorithm may not terminate. This can happen if the search space is infinite. It can also happen if the search space contains cycles. The latter case can be handled by checking for cycles in the algorithm. Thus Depth First Search is not complete.

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Advantages:• DFS consumes very less

memory space.• It will reach at the goal node in

a less time period than BFS if it traverses in a right path.

• It may find a solution without examining much of search because we may get the desired solution

• in the very first go.

Disadvantages:• It is possible that may states

keep reoccurring.• There is no guarantee of

finding the goal node.• Sometimes the states may also

enter into infinite loops.

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Difference between BFS and DFSBFS• It uses the data structure

queue.• BFS is complete because it

finds the solution if one exists.

• BFS takes more space i.e. equivalent to o (b0) where b is the maximum breath exist in a search

• tree and d is the maximum depth exit in a search tree.

• In case of several goals, it finds the best one.

DFS• It uses the data structure

stack.• It is not complete because it

may take infinite loop to reach at the goal node.

• The space complexity is O (d).

• In case of several goals, it will terminate the solution in any order.

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Uniform Cost Search

• This algorithm is by Dijkstra [1959]. The algorithm expands nodes in the order of their cost from the source.

• In uniform cost search the newly generated nodes are put in OPEN according to their path costs. This ensures that when a node is selected for expansion it is a node with the cheapest cost among the nodes in OPEN.

• Let g(n) = cost of the path from the start node to the current node n. Sort nodes by increasing value of g.

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Algorithm- Uniform Cost Search1. Initialize: set OPEN=s, CLOSED={} and c(s)=02. Fail: If OPEN={}, terminate with failure3. Select: Select a state with the minimum cost ,n, from OPEN and save in

CLOSED4. Terminate: If n G, terminate with success∈5. Expand: generate the successor of n

For each successor, m, :If m [OPEN CLOSED]∈ ∪set C(m)= C(n)+C(n,m) and insert m in OPENIf m [OPEN CLOSED]∈ ∪Set C(m)= min{ C(m),C(n)+C(n,m)}If c(m) has decreased and m CLOSED, move it to OPEN∈** if m is in OPEN already then we just simply update the cost**

6. Loop: Goto step 2

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Properties of UCSSome properties of this search algorithm are: • Complete • Optimal/Admissible • Exponential time and space complexity, O(bd)