Search Techniques in Artificial Intelligence

A measure of the computational resources (time and memory) an algorithm requires relative to the size of its input.

A type of problem where the goal is to find the best solution that satisfies constraints while optimizing a given objective function. Examples include minimizing costs, maximizing profits, or finding the shortest route.

A problem where the initial state, goal condition, and possible actions are known, and the system must find the sequence of actions to reach the goal state. This often involves dealing with constraints and partial observability.

A type of problem that involves finding an arrangement or solution that satisfies a set of given constraints. The goal is to find a solution that meets all specified conditions, but not just any solution.

A problem where the solution involves searching through a large space of possibilities, and the complexity of finding a solution grows exponentially with the size of the input. Naive approaches often lead to impractical runtime.

Depth-Limited Search is a variant of Depth First Search, but sets a limit, l, to the depth of the search tree to avoid expanding infinitely.

Iterative-Deepening Depth First Search (IDDFS) gradually increases the depth limit, starting from 0, and recomputes the search tree in each iteration. It combines advantages from both Breadth First Search and Depth First Search.

The attractiveness of a node in a search graph, compared to others, can be measured by an evaluation function, f(n). This function provides a cost estimate based on state information and the desired goal.

The cost estimation function, h(n), used in informed search to estimate the cost of reaching the goal from a given node, n.

A heuristic is a rule of thumb or strategy used to make decisions when information is incomplete, commonly used by humans and in AI search algorithms to guide decision-making.

A function that estimates the cost of the cheapest path from a given node to a goal state. It is used to guide search algorithms by providing an informed guess of the remaining cost.

A search algorithm that prioritizes expanding the node estimated to be closest to the goal. It uses the heuristic function to evaluate nodes.

The cost of reaching a node from the initial node. It represents the actual path taken to reach the current node.

A search algorithm that combines the cost to reach a node and the estimated cost to reach the goal. It aims to find the optimal path (shortest or least cost) by balancing exploration cost and potential future cost.

The estimated cost of reaching the goal state from a given node. It represents the cost based on heuristics rather than actual paths.

The function used in A* Search to evaluate nodes. It combines the actual cost of reaching a node (g(n)) and the estimated cost from that node to the goal (h(n)).

The ability of a search algorithm to find a solution (goal state) if one exists. A complete algorithm guarantees finding a solution in a finite search space.

The ability of a search algorithm to find the optimal solution (the best or shortest path) among all possible solutions.

A* Search is a widely used search algorithm that efficiently finds optimal paths in a graph or tree by combining the cost of reaching a node with a heuristic estimate of the cost to reach the goal from that node.

Admissibility in A* refers to the heuristic function never overestimating the actual cost to reach the goal. It ensures that the algorithm will not consider a node as reaching the goal until it's actually the best option.

Consistency in A* means that the heuristic function satisfies the triangle inequality. The cost to the goal from any node 'n' is at most the cost to a neighboring node 'n'' plus the heuristic difference of the two nodes. It ensures that the algorithm finds a truly optimal path, not just a path with the lowest f-score.

A* search is considered complete, meaning it guarantees finding the solution if one exists. It systematically explores the search space, ensuring that no possible path goes unchecked. This is useful for finding the most optimal route.

While A* Search is optimal when the heuristic is admissible and consistent, it can still be useful even if those conditions are not met. It can still find a solution efficiently. However, the solution may not be the absolute best one.

A* Search can be problematic for large search spaces due to its high memory complexity. O(b^d) indicates exponential growth in memory needed as the branching factor 'b' and depth 'd' of the search tree increase. This means that for complex problems, it may not have enough memory to store all the nodes needed.

IDA* (Iterative Deepening A* ) performs depth-first search with a cost threshold. It iteratively expands the search depth until it finds a solution with the desired cost. It's particularly useful for overcoming memory constraints.