Solving Problems by Search Chapter 3
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Questions and Answers

What are the five components of a search problem formulation?

  1. Initial state (S0), 2) Possible actions available at each state (Successor Function), 3) Transition model describing what each action does, 4) Goal test that detects the goal state, 5) Path cost expressed in terms of step cost

Which of the following dimensions are used to evaluate search strategies? (Select all that apply)

  • Optimality (correct)
  • Completeness (correct)
  • Space complexity (correct)
  • Time complexity (correct)

    • Uniform-Cost Search is identical to Breadth-First Search when all step costs are equal.

    True

    In Uniform-Cost Search, the node with the lowest ________ is expanded first.

    <p>path cost</p> Signup and view all the answers

    Match the search algorithm with its description:

    <p>Breadth-First Search = Expands nodes level by level, starting from the root node Uniform-Cost Search = Expands the node with the lowest path cost Depth-First Search = Explores as far as possible along each branch before backtracking</p> Signup and view all the answers

    What data structure is used to keep track of nodes to be explored in Uniform-cost search?

    <p>Priority Queue (Min-Heap)</p> Signup and view all the answers

    What is the primary purpose of Depth-First Search (DFS)?

    <p>To expand the deepest node first</p> Signup and view all the answers

    Depth-Limited Search (DLS) limits the expansion of nodes to a predetermined depth.

    <p>True</p> Signup and view all the answers

    Bidirectional search runs two simultaneous searches: one forward from the initial state and the other backward from the ____. The two searches meet in the middle.

    <p>goal</p> Signup and view all the answers

    What are the five components of a search problem formulation?

    <ol> <li>Initial state (S0), 2) Possible actions available at each state, 3) Transition model describing what each action does, 4) Goal test that detects the goal state, 5) Path cost expressed in terms of step cost</li> </ol> Signup and view all the answers

    Which of the following is a property used to evaluate search strategies?

    <p>Optimality</p> Signup and view all the answers

    Uniform-cost search expands the node with the highest path cost.

    <p>False</p> Signup and view all the answers

    What data structure is used as the frontier in Breadth-First Search?

    <p>Queue</p> Signup and view all the answers

    Match the following search algorithms with their descriptions:

    <p>Breadth-first search = Expands nodes at the shallowest level first Uniform-Cost Search = Expands the node with the lowest path cost</p> Signup and view all the answers

    What is the primary data structure used in Uniform-cost search?

    <p>Priority Queue (Min-Heap)</p> Signup and view all the answers

    Is Uniform-cost search optimal even if the higher-cost of identical nodes on the queue is not removed?

    <p>True</p> Signup and view all the answers

    What is the strategy followed by Depth-First Search?

    <p>expand a deepest node first</p> Signup and view all the answers

    In Depth-First Search, the frontier is represented as a:

    <p>LIFO stack</p> Signup and view all the answers

    Depth-limited search limits the search to a predetermined depth limit ___.

    <p>L</p> Signup and view all the answers

    Match the following search strategies with their primary characteristic:

    <p>DFS = Expand the deepest node first IDS = Combines depth-first search's space efficiency and breadth-first search's completeness BFS = Guarantees the shortest path in an unweighted graph</p> Signup and view all the answers

    Study Notes

    Solving Problems by Searching

    • A search problem consists of five components:
      • Initial state (S0)
      • Possible actions available at each state
      • Transition model describing what each action does
      • Goal test that detects the goal state
      • Path cost expressed in terms of step cost

    State-Space Graph

    • Graphs have vertices (nodes), edges (arcs), and directed arcs
    • State-space graphs:
      • States are vertices
      • Actions are directed arcs (carry state to state)

    Search Strategies

    • A search strategy is defined by the order of node expansion
    • Strategies are evaluated along the following dimensions:
      • Completeness: does it always find a solution if one exists?
      • Time complexity: number of nodes generated
      • Space complexity: maximum number of nodes in memory
      • Optimality: does it always find a least-cost solution?

    Types of Search Algorithms

    • Uninformed Search (Blind): only has the information provided by the problem formulation
    • Informed Search: has additional information that allows it to judge the promise of an action

    Uninformed Search Algorithms

    • Breadth-First Search (BFS)
    • Uniform-Cost Search (UCS)
    • Depth-First Search (DFS)
    • Depth-Limited Search (DLS)
    • Iterative Deepening Search (IDS)
    • Bidirectional Search

    Breadth-First Search (BFS)

    • Expands shallowest node first
    • Implementation: frontier is a FIFO queue
    • Strategy: expand a shallowest node first
    • Example: 8-puzzle

    Uniform-Cost Search (UCS)

    • Expands the node with the lowest path cost
    • Properties:
      • Processes all nodes with cost less than the cheapest solution
      • Takes time O(bC*/ε)
      • Has roughly the last tier, so O(bC*/ε)
      • Is complete?
      • Is optimal?
    • Frontier is a priority queue sorted by the cost

    Depth-First Search (DFS)

    • Expands the deepest node in the current fringe of the search tree
    • Strategy: expand a deepest node first
    • Implementation: frontier is a LIFO stack
    • Example: tree search

    Depth-Limited Search (DLS)

    • A variation of Depth-First Search (DFS) where the search is limited to a predetermined depth limit 𝐿
    • Useful when you want to avoid the potential infinite descent into deeper levels in a graph or tree

    Iterative Deepening Search (IDS)

    • Combines the depth-first search's space efficiency and breadth-first search's completeness
    • Performs a series of depth-limited searches with increasing depth limits
    • Ensures that the shortest path to the goal is found without consuming too much memory
    • Application: Artificial Intelligence in Games

    • Runs two simultaneous searches: one forward from the initial state and the other backward from the goal

    • Stopping when the two searches meet in the middle

    • Algorithm steps:

      1. Initialize: two queues and two sets
      2. Enqueue the initial nodes
      3. Search: alternately expand nodes from the front queue and the back queue
      4. Construct the path: once the meeting point is found, reconstruct the path from the start to the goal

    • Application: solving game trees in chess or checkers to a certain depth### Bidirectional Search

    • Bidirectional search is a combination of both forward and backward searches

    Comparing Uninformed Search Strategies

    • Breadth-First Search (BFS)
      • Useful when the solution is expected to be found at shallow depths
      • Guarantees the shortest path in an unweighted graph
    • Depth-First Search (DFS)
      • Memory-efficient
      • Useful when the solution is deep or the branching factor is large
    • Depth-Limited Search (DLS)
      • Addresses DFS's issue with infinite depth by imposing a limit
    • Iterative Deepening Depth-First Search (IDFS)
      • Combines the benefits of BFS's completeness and optimality with DFS's space efficiency
    • Uniform-Cost Search (UCS)
      • Ensures the least-cost path is found
      • Essential for problems where path costs vary

    Key Skills

    • Formulate a real-world problem as a search problem
    • Trace the execution and implement uninformed search algorithms
    • Explain space complexity, time complexity, and guarantees on the quality of the solution found for a given uninformed search algorithm
    • Determine whether and why it is appropriate to use an uninformed algorithm for a given scenario

    Solving Problems by Searching

    • A search problem consists of five components:
      • Initial state (S0)
      • Possible actions available at each state
      • Transition model describing what each action does
      • Goal test that detects the goal state
      • Path cost expressed in terms of step cost

    State-Space Graph

    • Graphs have vertices (nodes), edges (arcs), and directed arcs
    • State-space graphs:
      • States are vertices
      • Actions are directed arcs (carry state to state)

    Search Strategies

    • A search strategy is defined by the order of node expansion
    • Strategies are evaluated along the following dimensions:
      • Completeness: does it always find a solution if one exists?
      • Time complexity: number of nodes generated
      • Space complexity: maximum number of nodes in memory
      • Optimality: does it always find a least-cost solution?

    Types of Search Algorithms

    • Uninformed Search (Blind): only has the information provided by the problem formulation
    • Informed Search: has additional information that allows it to judge the promise of an action

    Uninformed Search Algorithms

    • Breadth-First Search (BFS)
    • Uniform-Cost Search (UCS)
    • Depth-First Search (DFS)
    • Depth-Limited Search (DLS)
    • Iterative Deepening Search (IDS)
    • Bidirectional Search

    Breadth-First Search (BFS)

    • Expands shallowest node first
    • Implementation: frontier is a FIFO queue
    • Strategy: expand a shallowest node first
    • Example: 8-puzzle

    Uniform-Cost Search (UCS)

    • Expands the node with the lowest path cost
    • Properties:
      • Processes all nodes with cost less than the cheapest solution
      • Takes time O(bC*/ε)
      • Has roughly the last tier, so O(bC*/ε)
      • Is complete?
      • Is optimal?
    • Frontier is a priority queue sorted by the cost

    Depth-First Search (DFS)

    • Expands the deepest node in the current fringe of the search tree
    • Strategy: expand a deepest node first
    • Implementation: frontier is a LIFO stack
    • Example: tree search

    Depth-Limited Search (DLS)

    • A variation of Depth-First Search (DFS) where the search is limited to a predetermined depth limit 𝐿
    • Useful when you want to avoid the potential infinite descent into deeper levels in a graph or tree

    Iterative Deepening Search (IDS)

    • Combines the depth-first search's space efficiency and breadth-first search's completeness
    • Performs a series of depth-limited searches with increasing depth limits
    • Ensures that the shortest path to the goal is found without consuming too much memory
    • Application: Artificial Intelligence in Games

    Bidirectional Search

    • Runs two simultaneous searches: one forward from the initial state and the other backward from the goal

    • Stopping when the two searches meet in the middle

    • Algorithm steps:

      1. Initialize: two queues and two sets
      2. Enqueue the initial nodes
      3. Search: alternately expand nodes from the front queue and the back queue
      4. Construct the path: once the meeting point is found, reconstruct the path from the start to the goal

    • Application: solving game trees in chess or checkers to a certain depth### Bidirectional Search

    • Bidirectional search is a combination of both forward and backward searches

    Comparing Uninformed Search Strategies

    • Breadth-First Search (BFS)
      • Useful when the solution is expected to be found at shallow depths
      • Guarantees the shortest path in an unweighted graph
    • Depth-First Search (DFS)
      • Memory-efficient
      • Useful when the solution is deep or the branching factor is large
    • Depth-Limited Search (DLS)
      • Addresses DFS's issue with infinite depth by imposing a limit
    • Iterative Deepening Depth-First Search (IDFS)
      • Combines the benefits of BFS's completeness and optimality with DFS's space efficiency
    • Uniform-Cost Search (UCS)
      • Ensures the least-cost path is found
      • Essential for problems where path costs vary

    Key Skills

    • Formulate a real-world problem as a search problem
    • Trace the execution and implement uninformed search algorithms
    • Explain space complexity, time complexity, and guarantees on the quality of the solution found for a given uninformed search algorithm
    • Determine whether and why it is appropriate to use an uninformed algorithm for a given scenario

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    Description

    This quiz covers the formulation of search problems, including initial states, possible actions, transition models, goal tests, and path costs. It's essential for goal-based agents in fully observable, deterministic, sequential, static, discrete, and single-agent environments.

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