Search Algorithms in AI

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Questions and Answers

What is the time complexity associated with iterative deepening search (IDS)?

O(bd/2)

O(bl)

O(bm)

O(bd) (correct)

Which search method is generally preferred for large state spaces when the solution depth is unknown?

Depth-first search

Greedy search

Breadth-first search

Iterative deepening search (correct)

What characterizes bidirectional search?

It requires knowledge of the solution state. (correct)

It uses a single search tree.

It only works in heuristic search environments.

It eliminates the need for depth limit.

What is a primary advantage of using bidirectional search?

It reduces the search depth needed. Signup and view all the answers

Which search strategy is not complete?

Depth-first search Signup and view all the answers

What is the primary difficulty associated with bidirectional search?

It sometimes requires tracking all paths. Signup and view all the answers

Which of the following statements about the time complexity of bidirectional search is accurate?

It is equal to O(bd/2). Signup and view all the answers

What is the space complexity of depth-first search (DFS)?

O(bm) Signup and view all the answers

What is the main feature of Depth-First Search (DFS)?

It explores the deepest node first before backtracking. Signup and view all the answers

What problem can arise with the Depth-First Search approach?

It can go on indefinitely down one path. Signup and view all the answers

What is a common solution to the issues faced in Depth-First Search?

Imposing a depth limit on the search. Signup and view all the answers

In the context of the 8-puzzle, what is the objective of using 'move blank' operations?

To generate new states towards reaching the goal state. Signup and view all the answers

What is the characteristic of Breadth-First Search (BFS)?

It explores all nodes at the current depth before moving deeper. Signup and view all the answers

Which statement accurately reflects the difference between DFS and BFS?

BFS is often faster than DFS for shallow trees. Signup and view all the answers

In the search strategies, what is a defining characteristic of uninformed search techniques?

They expand nodes without any knowledge about the goal's proximity. Signup and view all the answers

What is one drawback of uninformed search strategies like BFS and DFS?

They may consume a large amount of memory. Signup and view all the answers

Which of the following describes a Breadth-First Search (BFS) traversal?

Explores all nodes at the present depth prior to moving on to the nodes at the next depth level. Signup and view all the answers

What is the primary difference between Depth-First Search (DFS) and Breadth-First Search (BFS)?

BFS explores all branches at the present depth before proceeding while DFS goes as deep as possible down one branch. Signup and view all the answers

Which of the following is NOT considered an uninformed search strategy?

A* Search Signup and view all the answers

In the context of graph search algorithms, which characteristic defines an informed (heuristic) search strategy?

It uses heuristics to estimate the cost of reaching the goal. Signup and view all the answers

Which type of edge exists if (u,v) is part of the original graph but not the spanning tree, and u is neither a descendant nor an ancestor of v?

Cross Edge Signup and view all the answers

When performing Bidirectional Search, what is a critical requirement for the two searches to converge?

The goal must be the same for both searches. Signup and view all the answers

What is the main advantage of using Depth-Limited Search (DLS) compared to standard Depth-First Search (DFS)?

DLS prevents infinite paths from being explored due to depth limits. Signup and view all the answers

Which statement accurately represents a characteristic of the Minimum Spanning Tree (MST)?

It is a connected acyclic subgraph that minimizes the total edge weight. Signup and view all the answers

Study Notes

Lecture 3 - Part 1: Search in Problem Solving

Goal-based agents are used in problem-solving
Lecture is about search in problem solving
Search methods for state space are covered
Uninformed and informed search algorithms are discussed
Graph theory review is part of the lecture

Important Chapter Summary

Uninformed search strategies include Breadth-First Search (BFS) and Depth-First Search (DFS)
Informed search strategies include Uniform-Cost Search (UCS), Best-First Search, and A* search
Depth-First Iterative deepening (IDS) and Bidirectional search (BS) are also discussed
Time and space complexity for each algorithm are included

Lecture Outline (Chapter 3)

Graph theory is briefly reviewed
Strategies for state space search are outlined
Uninformed search algorithms are discussed
Informed search algorithms are discussed
Asymptotic complexity (Big O) is reviewed

Recap: Predicate Calculus

Predicate calculus expressions offer well-defined formal semantics and sound and complete inference rules
Predicate calculus is a good representation language

Objectives: Problem-Solving Agent

Agents act by setting goals and considering actions to achieve them
A problem is a goal and the means to achieve it
Search is the process of exploring the means to achieve a goal

Search for Solutions (Generate and Test)

Generating action sequences is a key part of search
Data structures for search trees are important

Search Strategies (Properties of Search Methods)

Completeness: guaranteeing all solutions are found
Time complexity: the time taken for a search
Space complexity: memory used for a search
Optimality: finding the best/optimal solution
Admissibility: finding the optimal solution quickly
Irrevocability: potentially finding suboptimal solutions

Search Technique/Algorithms

Breadth-First Search (BFS)
Depth-First Search (DFS)

Search Problems in the Algorithm Class

Sequential Search
Binary Search
N-Queen Problem
Sum-of-Subsets Problem
Graph Coloring Problem
Hamiltonian Circuits Problem
0-1 Knapsack Problem
Traveling Salesperson Problem

Search Questions

Is the problem solver guaranteed to find a solution?
Will the problem solver always terminate?
When a solution is found is it guaranteed to be optimal?
What is the complexity of the search process in terms of time and memory usage?
How can the interpreter most effectively reduce search complexity?
How can an interpreter be designed to efficiently use a representation language?

Goal-Based Agents

Goal-based agents succeed by considering future actions and their outcomes
Problem-solving agents find sequences that lead to desirable states
General-purpose search algorithms can solve these problems

Goal-Driven Search vs Data-Driven Search

Goal-Driven search starts at the goal and works backwards
Most search methods are data-driven, starting from an initial state

Examples of Search Problems

Chess: looking for a move to improve position
Route planning: minimizing distance between locations
Theorem proving: finding reasoning steps to prove a theorem
Machine learning: finding a concept to categorize

Search Terminology

States: places the search can visit
Search space: set of possible states
Search path: the states the agent actually visits
Solution: a state accomplishing the problem
Strategy: choosing the next step in a path
Goal formulation: deciding the actions and states to consider; given a goal
Problem formulation: deciding what actions and states to consider given a goal
Search: the exploration process

Well-Defined Problems and Solutions

A problem is defined by four components:
- Initial state
- Actions
- Goal test
- Path cost

Specifying a Search Problem

Initial state: tracking visited states
Operators: functions that change states
Goal test: determining if search succeeded

Two types of Search Algorithms

Uninformed search algorithms have no problem information other than its definition
Informed search algorithms have some idea of where to look for solutions

General Search Considerations

Path or artefact: is it the route or destination
Completeness: finding all solutions
Time and space trade-offs: balancing speed and memory
Soundness: ensuring found solutions are valid
Additional information: extra data for the agent

Measuring Problem-Solving Performance

Completeness
Optimality
Time complexity
Space complexity

Graph and Agenda Analogies

Graph analogy: states are nodes, operators are edges
Agenda analogy: (State, Operator) pairs are put onto an agenda; operator used to generate new state from a given state

Example Problem

Goal: finding a boy's name from letters D, N, A
Initial state: empty string
Searching, Operators, and Goal testing

Uniform Search Strategies

Breadth-First Search (BFS)
Depth-First Search (DFS)

Breadth-First Search (BFS)

New state, S, reached, agenda items placed at bottom of the agenda
Graph Analogy: expanding a node level by level

Exercise: Web Spidering

BFS is preferred for web spidering because the web is assumed to be connected

Graph Theory Review (Data Structures)

Graph Terminology

Graph: G=(V,E)
Vertex set: V
Edge set: E (adjacent vertices)

Directed and Undirected Graphs

Directed graphs have ordered pairs (u, v) for edges
Undirected graphs have unordered pairs {u, v} for edges

Proper Graphs and Subgraphs

Paths in Graphs

Simple Paths and Cycles

A Connected Undirected Graph

Connected Components of an Undirected Graph

Biconnected Undirected Graphs

Size of a Graph

Representing a Graph by an Adjacency Matrix

Adjacency List Representation of a Graph

Definition of an Undirected Tree

Definition of a Directed Tree

An Ordered Tree

An Ordered Tree (Definition)

An Ordered Tree (Types)

Tree Traversal (Preorder)

Tree Traversal (Inorder)

Tree Traversal (Postorder)

Exercise: Tree Traversal

Spanning Tree

Example Spanning Tree of a Graph

Classification of Edges of G with Spanning Tree T

Minimum Spanning Tree (MST)

Examples

Search Strategies

Uninformed Search Strategies

Breadth-First Search (BFS) (Genetic Professor's Son Name)

An example for BFS

BFS Exercise

BFS of the 8-puzzle

DFS Property

An example for DFS

DFS Exercise

DFS vs BFS

Recap: Breadth-First Search (BFS)

Depth-Limited Search

Iterative Deepening (Depth-first) Search (IDS)

IDS

Bidirectional Search

Bidirectional Search ...

Comparing Uninformed Search Strategies

Uninformed Search?

Uniform Cost Search (UCS)

Difference: Best-first search, UCS, and A*