Understanding Search Algorithms: Techniques, Complexity & Use Cases


Introduction

Artificial Intelligence (AI) is getting machines to think and behave smartly, and much of this smartness is all about problem-solving. From finding one’s way around a city to defeating an opponent at chess to solving the Rubik’s Cube, a smart system needs to make choices given a list of options and limitations. Search algorithms enter the picture here.

Search in AI is navigating a problem space to reach a goal state. It can be imagined as moving from one node to another within a tree or graph in which the nodes are states and the actions are edges. Selecting the right path is crucial for effective problem-solving, particularly when navigating complex environments, limited resources, or time constraints.

Search procedures are generally classed into two categories:

  • Uninformed search: These searches the search space without using any knowledge of the domain regarding how close a node is to the goal. They are straightforward and systematic but usually inefficient.
  • Heuristic search: These utilize heuristics – rules of thumb or approximations – to more intelligently direct the search to the solution.

These search algorithms are the basis for disciplines like robotics, video games, navigation, puzzle solving, and planning. In this blog, we will guide you through some of the most popular search methods used in AI, such as Breadth-First Search, Depth-First Search, A*, and Greedy Search, and show you real-life examples and diagrams of how they operate.

1.    Uninformed (Blind) Search

Uninformed search strategies work without any domain knowledge. They search systematically from nodes until a solution is reached, though they can be ineffective for larger spaces.

Types of Uninformed Search

The following are the types of Uninformed Search

a.      Breadth-First Search (BFS)

BFS visits all the nodes at a particular depth before moving to the next depth level to ensure the shortest path (in terms of the number of edges) in unweighted graphs.

Breadth-First Search algorithm visualized on a graph with node expansion order
Breadth-First Search (BFS)

Complexity

The time and space complexity of the BFS is O (bm), where m is the maximum depth and b is the branching factor.

Use Case

BFS is used in tree searching.

b.     Depth-First Search (DFS)

DFS goes as deep as possible along a single branch before backtracking. It uses little memory but isn’t optimal, and can get into infinite loops in circular spaces.

Depth-First Search algorithm visualized on a graph with node expansion order
Depth-First Search

Complexity

The time complexity of the DFS is O(bm), where m is the maximum depth.

The space complexity of the DFS is O(b.m), keeping one path in memory at a time.

Use Case

DFS is used for solving puzzles when there are deep solutions but not enough memory.

c.      Iterative Deepening (IDDFS)

IDDFS unites Breadth-First Search’s completeness/ optimality with Depth-First Search’s space efficiency. It does DFS to depth 0, 1, 2,... incrementally until a goal is reached.

Complexity

The time complexity of the IDDFS is still O(bd), but with the additional overhead of repeated execution of shallower searches.

Whereas the space complexity of IDFFS is O(b.d)

Use Case

IDDFS is useful in scenarios where the depth of the solution is now known or potentially infinite, and memory is a constraint.

Comparison of Uninformed Methods

Comparison table of AI search algorithms showing completeness, optimality, time, and space complexity for BFS, DFS, and IDDFS

Uninformed searches are easy but unsuitable for large-scale problems, which encourages the use of heuristic methods.

2.    Heuristic (Informed) Search

Heuristic search applies problem-specific knowledge (heuristic) to direct the search toward the goal more effectively.

Types of Heuristic Search The following are the types of Heuristic search:

a.      Greedy Best-First Search

Greedy search chooses the node nearest to the goal using the heuristic value h(n) (estimated distance to goal).

The advantage of this search is that it is very Quick.

This type of search is not optimal and can be trapped in cycles or dead ends if the heuristic is poor.

Complexity

The space and time complexity of the greedy best-first search is O(bm), where b represents the branching factor (the maximum number of children a node has) and m is the maximum depth of the search space.

Use Case

Greedy Best-First Search is usually used in pathfinding in video games.                                                                                                                                       

b.     A* Search

A* integrates path cost g(n) (cost to date) and heuristic h(n) (estimated cost to goal) into evaluation function f(n)=g(n) + h(n)

This type of search never overestimates the true cost to reach the goal; the algorithm is guaranteed to find the optimal solution.

Complexity

The complexity of the A* search algorithm depends on heuristic accuracy and branching factor. The space complexity of the algorithm is O(bd).

Use Case

This type of search algorithm is used in navigation, game AI, and network routing.

c.      Route Planning with A*

A* is crucial in navigation, such as maps or games. Example:

  • Heuristic: Straight-line distance (Euclidean)
  • Cost: Weights on road nodes connected by edges.
  • Goal: To determine the shortest path between two cities.

The application is widespread in GPS, robotics, and game AI.

d.     IDA * (Iterative Deepening A*)

IDA* uses A* evaluation in ascending cost limits, marrying the benefit of A*’s optimality with IDDFS’s better space efficiency.

  • Advantages: Utilizes Linear memory only.
  • Disadvantages: Visits the same node multiple times.
Use Case

It is used in finding puzzles such as the 15-puzzle, where the storage of the full path is impractical.

Real-World Applications in Games and Problem Solving:

These search methods drive much AI functionality:

  1. Maize Navigation: A* computes the shortest path.
  2. Board Games: IDDFS applies to deep game trees.
  3. Robot Planning: Greedy search computes near-optimal paths fast.
  4. Puzzle Solvers: A* and IDA* generate fast optimal solutions.

Conclusion

Search algorithms from the core of intelligent problem-solving in AI. From finding routes through mazes and puzzles to playing intricate games of strategy and mapping out optimum journeys, these methods grant machines the power to think several steps ahead, weigh up alternatives, and make rational decisions.

Naive search algorithms like Breadth-First Search and Depth-First Search provide a systematic means of visiting all possible paths, although they tend not to be efficient in big or infinite search spaces. Improvements like Iterative Deepening assist in merging the strengths of both breadth and depth approaches. Conversely, heuristic search algorithms such as Greedy Search and A* add a level of intelligence by approximating the cost of reaching the goal, leading to much better performance in most real-world applications.

Sophisticated algorithms such as IDA* improve memory efficiency further without losing informed search properties, holding them well-suited for environments with limited resources.

As it continues to advance, search-based problem-solving is still relevant – not just as a starting point for constructing intelligent systems but as an applied technique in areas like robotics, logistics, and game design. Learning these algorithms paves the way to developing smarter, more flexible, and goal-driven systems that can traverse the complexities of our real and virtual worlds.

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