![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 Search
1. Initialize: set OPEN=s, CLOSED={} and c(s)=0
2. Fail: If OPEN={}, terminate with failure
3. Select: Select a state with the minimum cost ,n, from OPEN and save in
CLOSED
4. 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 OPEN
If 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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Lecture 08 uninformed search techniques
- 1. Uninformed Search Techniques Lecture-08 Hema Kashyap 1
- 2. Uninformed Search Breadth First Search Uniform Cost Search Depth First Search Depth Limited Search Iterative deepening Depth First Search Bidirectional Search 2
- 4. Concept Step 1: Traverse the root node Step 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. 4
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- 11. 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. 11
- 12. 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. 12
- 13. 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. 13 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.
- 15. Concept Step 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. 15
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- 19. Step 4: Node D is removed from fringe. C and F are pushed in front of fringe 19
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- 21. 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. 21
- 22. 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. 22
- 23. 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. 23 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.
- 24. Difference between BFS and DFS BFS • 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. 24 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.
- 25. 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. 25
- 26. Algorithm- Uniform Cost Search 1. Initialize: set OPEN=s, CLOSED={} and c(s)=0 2. Fail: If OPEN={}, terminate with failure 3. Select: Select a state with the minimum cost ,n, from OPEN and save in CLOSED 4. 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 OPEN If 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 26
- 27. Properties of UCS Some properties of this search algorithm are: • Complete • Optimal/Admissible • Exponential time and space complexity, O(bd) 27