Artificial Intelligence: Uninformed Search Strategies

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Questions and Answers

What are the limitations of Depth-First Search (DFS) regarding optimality and completeness?

DFS is neither complete nor optimal; it may get stuck in infinite branches and does not guarantee the shortest path.

How does Uniform Cost Search (UCS) differ from Breadth-First Search (BFS)?

UCS considers path costs when expanding nodes, while BFS treats all nodes equally without considering cost.

What impact does the branching factor have on the time complexity of DFS?

The time complexity of DFS is O(b^m), where m is the maximum depth, and the branching factor directly influences the number of nodes explored.

Explain how Depth-Limited Search (DLS) prevents infinite loops?

<p>DLS prevents infinite loops by setting a depth limit, beyond which it does not expand any nodes.</p> Signup and view all the answers

What are the complexities of Uniform Cost Search in terms of time and space?

<p>UCS has a time complexity of O(bC*/ε) and a similar space complexity, as it stores all frontier nodes.</p> Signup and view all the answers

Why is Uniform Cost Search considered optimal and complete?

<p>UCS is optimal because it expands nodes in increasing order of path cost and complete if all costs are positive and the branching factor is finite.</p> Signup and view all the answers

In what scenarios is Depth-Limited Search preferred over standard DFS?

<p>DLS is preferred in scenarios with infinite paths or deep paths that could lead DFS to loop indefinitely.</p> Signup and view all the answers

What is the main advantage of using a priority queue in Uniform Cost Search?

<p>The priority queue allows UCS to efficiently expand the least-cost node first, ensuring optimal pathfinding.</p> Signup and view all the answers

What is the time complexity of Breadth-First Search (BFS), and how does it affect its practicality?

<p>The time complexity of BFS is O(b^d), which makes it time-intensive as the depth, d, increases.</p> Signup and view all the answers

Explain why Depth-First Search (DFS) is not optimal in finding solutions.

<p>DFS can return solutions that are not the shortest or least costly because it does not prioritize paths based on cost.</p> Signup and view all the answers

What condition must be met for Uniform Cost Search (UCS) to be considered complete?

<p>UCS is complete if the branching factor is finite and all step costs are positive.</p> Signup and view all the answers

How does the space complexity of Depth-Limited Search (DLS) compare to that of Depth-First Search (DFS)?

<p>The space complexity of DLS is O(b×l), which is similar to DFS's O(b×m), as both store nodes along the current path.</p> Signup and view all the answers

What is the primary advantage of Iterative Deepening Depth-First Search (IDDFS) over traditional Depth-First Search (DFS)?

<p>IDDFS combines the space efficiency of DFS with the completeness of BFS, effectively exploring all depths incrementally.</p> Signup and view all the answers

In what scenarios might Uniform Cost Search (UCS) be slower than Breadth-First Search (BFS)?

<p>UCS may be slower than BFS when it explores nodes with costs lower than the cost of the optimal solution but does not lead directly to a goal.</p> Signup and view all the answers

Describe the completeness of Depth-First Search (DFS) in relation to infinite search spaces.

<p>DFS is not complete for infinite or cyclic search spaces, as it may get stuck in an endless path.</p> Signup and view all the answers

What condition makes Iterative Deepening Depth-First Search (IDDFS) optimal?

<p>IDDFS is optimal if all steps have equal costs, as it explores solutions at shallower depths first.</p> Signup and view all the answers

What is the main advantage of Iterative Deepening Search (IDS) over traditional Depth-First Search (DFS)?

<p>IDS is more memory-efficient than DFS and combines the completeness of BFS with the space efficiency of DFS.</p> Signup and view all the answers

Explain how Bidirectional Search improves search efficiency compared to unidirectional searches.

<p>It simultaneously searches from both the start and goal nodes, effectively halving the search depth and reducing the number of nodes expanded.</p> Signup and view all the answers

What conditions must be met for Bidirectional Search to be considered optimal?

<p>Bidirectional Search is optimal if both searches use BFS or UCS with consistent costs.</p> Signup and view all the answers

Discuss the time and space complexity of Breadth-First Search (BFS).

<p>BFS has a time complexity of O(b^d) and a space complexity of O(b^d) due to storing all nodes at the current depth.</p> Signup and view all the answers

How does the completeness of BFS differ when the branching factor is infinite?

<p>BFS is complete only if the branching factor is finite; with infinite branching, it may not explore all nodes.</p> Signup and view all the answers

In what scenario is Iterative Deepening Search (IDS) optimal?

<p>IDS is optimal when each action cost is uniform because it finds the shallowest solution.</p> Signup and view all the answers

What distinguishes Depth-First Search (DFS) from Breadth-First Search (BFS) in terms of memory usage?

<p>DFS is generally more memory-efficient than BFS, as it only needs to store a path from the root to a leaf.</p> Signup and view all the answers

What is the time complexity of Bidirectional Search and why is it considered efficient?

<p>The time complexity is O(b^(d/2)), as it effectively halves the search depth, leading to fewer nodes to expand.</p> Signup and view all the answers

Flashcards

BFS Time Complexity

The time it takes for Breadth-First Search to complete, increasing with graph depth.

BFS Space Complexity

The memory BFS uses; in the worst-case scenario, it grows exponentially with the graph's depth.

DFS Completeness

DFS isn't always guaranteed to find a solution in infinite or cyclical graphs without a depth limit

DFS Optimality

DFS doesn't always find the shortest or lowest-cost solution

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DFS Time Complexity

The computational time for DFS increases exponentially with the maximum depth of the search.

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DFS Space Complexity

Memory usage of DFS is proportional to the maximum depth of the search.

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UCS Completeness

Uniform Cost Search is complete if branching factors are finite, and costs are positive.

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UCS Optimality

Uniform Cost Search is optimal as it expands nodes in order of increasing cost.

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Iterative Deepening Search (IDS)

An uninformed search algorithm that combines the completeness of Breadth-First Search (BFS) with the space efficiency of Depth-First Search (DFS). It performs multiple depth-limited searches, gradually increasing the depth limit until a solution is found.

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IDS Complexity: Time

O(b^d), similar to BFS. This means the time taken grows exponentially with the depth of the solution (d) and branching factor (b).

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IDS Complexity: Space

O(b*d), more memory-efficient than BFS. It only needs to store nodes at the current search depth.

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Bidirectional Search

A search technique that simultaneously expands nodes from both the start and goal nodes to meet in the middle, aiming to reduce search time.

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Bidirectional Search: Complexity Time

O(b^(d/2)), effectively halves the search depth compared to BFS. This is because the search effort is split between two fronts.

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Bidirectional Search: Complexity Space

O(b^(d/2)) for both fronts. While still memory-intensive, it's generally more efficient than BFS alone.

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What is DFS?

Depth-First Search (DFS) explores a tree or graph by going as deep as possible along each branch before backtracking. It prioritizes depth over breadth.

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What is DFS's Time Complexity?

The time DFS takes grows exponentially with the maximum search depth (b^m). This makes it inefficient for very deep searches.

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What is DFS's Space Complexity?

DFS only stores nodes along the current path, making it more space-efficient than BFS. Its space usage is proportional to the maximum depth (b*m).

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What is UCS?

Uniform Cost Search (UCS) finds the least-cost path in a graph by expanding nodes in increasing order of path cost. It's optimal for finding the cheapest route.

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What is UCS's Time Complexity?

UCS's complexity depends on the cost of the optimal solution (C*) and minimum action cost (ε). It grows proportionally to (bC*/ε).

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What is UCS's Space Complexity?

Similar to its time complexity. UCS stores all frontier nodes, which can become large for high-cost solutions. It's similar to (bC*/ε).

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What is DLS?

Depth-Limited Search (DLS) restricts DFS by setting a maximum depth. It's useful for graphs with infinite branches or extremely deep paths.

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What is DLS's Time Complexity?

The time DLS takes depends on the depth limit (l) and is represented as (b^l). The more levels you search, the slower it gets.

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Study Notes

Assignment Information

  • Submitted by: Zainab Latif
  • Submitted to: Prof. Usama
  • Course code: COSC-2112
  • Course title: Artificial Intelligence
  • Department: ADP(CS)
  • Assignment No: 01

Uninformed Search Strategies

  • Uninformed search strategies are basic algorithms used in AI and problem-solving tasks where no specific domain knowledge is used.
  • They explore paths systematically to find the optimal solution.
  • Key strategies include Breadth-First Search (BFS), Uniform Cost Search (UCS), Depth-First Search (DFS), and Depth-Limited Search (DLS).

Breadth-First Search (BFS)

  • Principle: Explores the search space level by level, expanding nodes in order of their depth from the root. Prioritizes nodes with the fewest steps taken from the start.
  • How it operates: Uses a FIFO (First-In, First-Out) queue data structure. Starts with the root, adds immediate neighbors to the queue, dequeues and expands one level at a time. Unvisited successors are enqueued. Continues until a goal node or empty queue is found.
  • Optimality and Completeness: Complete (if a solution exists, it will be found) and optimal (shortest path) if all actions have the same cost.
  • Complexity: Time Complexity: O(bd), where b is branching factor and d is the depth of the solution. Space Complexity: O(bd).

Depth-First Search (DFS)

  • Principle: Explores each branch of the search tree as deeply as possible before backtracking. Useful when memory is a constraint, only keeps track of nodes on the current path.
  • How it operates: Uses a stack (or recursion). Starts at the root, adds unexplored neighbors to the stack. Pops nodes from the stack and expands. Pushes successors onto the stack, continuing until goal or dead end. Backtracks to the most recent unvisited node when a dead end is encountered.
  • Optimality and Completeness: Neither complete (may get stuck in infinite branch) nor optimal (doesn't guarantee shortest path).
  • Complexity: Time Complexity: O(bm) where m is the maximum depth. Space Complexity: O(bm) where m is the maximum depth.

Uniform Cost Search (UCS)

  • Principle: Generalizes BFS by considering path cost associated with each node. Ensures nodes are expanded in increasing order of path cost. Optimal for finding the least-cost path with varying costs.
  • How it operates: Uses a priority queue to keep track of nodes, ordered by their path cost from the start node. Expands the lowest-cost node, updating the queue.
  • Optimality and Completeness: Both complete (if finite branching & positive costs) and optimal (guarantees least-cost solution).
  • Complexity: Time Complexity: O(bC*/É›); Space Complexity: Similar to time complexity.

Depth-Limited Search (DLS)

  • Principle: Variant of DFS; limits the depth of the search, useful in cases where infinite or excessively deep paths could cause DFS loops.
  • How it operates: Uses a depth limit and applies DFS up to that limit, stopping expansion of nodes that exceed this depth. Similar to DFS, operating in a "last in, first out" manner.
  • Optimality and Completeness: Complete if the goal exists within the depth limit. Not optimal.
  • Complexity: Time Complexity: O(bl); Space Complexity: O(bl).

Iterative Deepening Depth-First Search (IDDFS)

  • Principle: Combines advantages of BFS's completeness and DFS's space efficiency by incrementally deepening the depth limit.
  • How it operates: Starts with a depth limit of 0, conducting a depth-limited search. Continues this until a goal node is found within a given depth.
  • Optimality and Completeness: Both complete and optimal for uniform costs.
  • Complexity: Time Complexity: O(bd); Space Complexity: O(bd).
  • Principle: Simultaneously searches forward from the start node and backward from the goal node, aiming to meet in the middle.
  • How it operates: Conducts two searches: forward from the start and backward from the goal. Methods used for frontiers include BFS, UCS. Finds solution (or determines no solution) faster than either BFS or DFS alone.
  • Optimality and Completeness: Complete and optimal if BFS / UCS is used for both directions.
  • Complexity: Time Complexity: O(bd/2); Space Complexity: O(bd/2).

Case Study: Shortest Path in a Graph

  • Example using BFS, DFS, UCS, and DLS to find shortest path in an unweighted grid.
  • Algorithm efficiency differences highlighted.

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