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Questions and Answers

Given a search space represented as a directed graph with cycles, which of the following modifications to a standard Depth-First Search (DFS) algorithm is LEAST likely to prevent infinite loops and redundant node revisits?

Implementing iterative deepening depth-first search (IDDFS) to progressively increase the depth limit.
Introducing a heuristic function to prioritize nodes closer to the goal state, guiding the search away from cycles. (correct)
Limiting the maximum depth of the search to a predetermined threshold, irrespective of the graph's diameter.
Employing a 'visited' set to track nodes already explored, preventing re-exploration of marked nodes.

In a Depth-First Search (DFS) implementation on a graph with no known depth limit, the space complexity is guaranteed to be superior to that of Breadth-First Search (BFS) regardless of the graph's structure and connectivity.

False (B)

Consider a directed graph representing state transitions in a complex automated planning problem. Describe a pragmatic modification to the standard Depth-First Search (DFS) algorithm to mitigate the risk of non-termination in the presence of cycles, without completely sacrificing the algorithm's space efficiency. Explain the trade-offs involved.

A practical modification involves implementing a 'depth threshold' and a 'cycle detection' mechanism. The depth threshold limits the maximum path length explored, preventing infinite loops along excessively long paths. Simultaneously, maintain a stack of visited nodes along the current path; if a node is encountered that's already on the stack, it indicates a cycle, and the search backtracks. The trade-off is introducing incompleteness (the algorithm might miss solutions beyond the depth threshold) and added computational overhead for cycle detection, balanced against guaranteed termination and reduced space consumption compared to exhaustive search strategies.

In the context of graph search algorithms, the phenomenon where a simple tree search revisits the same nodes of a graph, potentially leading to infinite loops, highlights its inadequacy for handling ______ representations of problem spaces.

cyclic Signup and view all the answers

In the context of uninformed search algorithms, which statement accurately characterizes their primary limitation when applied to complex problem domains with expansive state spaces?

The computational cost of uninformed search algorithms increases exponentially with the depth of the search tree, thus rendering them practically infeasible for problems exceeding a modest scale. (D) Signup and view all the answers

Match the following characteristics to their corresponding search algorithms:

Completeness: No, Time complexity: $b^d$ = Depth-First Search Potential for non-termination in graphs with infinite paths = Depth-First Search Space complexity: bd (better than BFS) = Depth-First Search May suffer from repetition of states in graph searches if not modified. = Depth-First Search Signup and view all the answers

In the 8-Queens problem, an admissible heuristic for A* search would be the number of pairs of queens that are attacking each other, as it never overestimates the remaining cost to reach the goal state.

False (B) Signup and view all the answers

Explain, using concepts from computational complexity theory, why certain classical AI problems, such as the Traveling Salesperson Problem (TSP), are considered particularly challenging and often require heuristic or approximation algorithms in practice.

The Traveling Salesperson Problem is NP-hard, meaning that no polynomial-time algorithm is known that can solve it optimally. Therefore, exact solutions are computationally intractable for large instances, necessitating the use of heuristic or approximation algorithms to find reasonably good solutions within practical time limits. Signup and view all the answers

In the context of constraint satisfaction problems, the Minimum Remaining Values (MRV) heuristic aims to select the variable with the fewest ______ values.

legal Signup and view all the answers

Match the following search algorithms with their completeness and optimality properties:

Breadth-First Search = Complete and optimal if path cost is a non-decreasing function of node depth. Depth-First Search = Not complete and not optimal. A* Search = Complete and optimal if the heuristic is admissible and consistent. Iterative Deepening Search = Complete and optimal if the branching factor is finite and path cost is uniform. Signup and view all the answers

Consider a variant of the Missionaries and Cannibals problem where the boat's capacity changes dynamically based on the number of trips made. How would this modification affect the state space representation and the complexity of finding an optimal solution?

The state space expands to include the boat's evolving capacity, necessitating alterations to the successor function and potentially impacting solution optimality. (C) Signup and view all the answers

Critically evaluate the applicability of using a brute-force search strategy for solving a crypt-arithmetic puzzle, given that the puzzle involves assigning digits (0-9) to distinct letters in a mathematical equation. Quantify the search space and discuss the computational implications.

For a crypt-arithmetic puzzle with N distinct letters, the search space size is on the order of $10! / (10-N)!$. This represents the number of ways to assign distinct digits to the letters. Brute-force search would explore all these possibilities, which may be viable for small N. However, as N increases, the computation becomes intractable, making the brute force approach infeasible. Signup and view all the answers

In the context of VLSI layout optimization, which of the following best describes the primary objective function being minimized when employing search algorithms?

Minimizing total interconnect length, signal propagation delay, and power consumption, subject to constraints on die area and manufacturing yield. (B) Signup and view all the answers

In a route-finding problem, if a search algorithm is complete and the path cost is defined as zero for all states except the final state, then any solution found by the algorithm is guaranteed to be optimal.

True (A) Signup and view all the answers

Formally define, using set notation, the search space within the context of a general search problem represented as a graph, given an initial state σ, a set of actions A, and a transition model T.

Let $\Sigma_0 = {\sigma}$ be the initial set of states. Define $\Sigma_{i+1} = \Sigma_i \cup {T(\sigma', a) \mid \sigma' \in \Sigma_i, a \in A}$. The search space $\Sigma^$ is the closure of this process, i.e., $\Sigma^ = \bigcup_{i=0}^{\infty} \Sigma_i$. Signup and view all the answers

In bi-directional search, the space complexity is typically $O(b^{d/2})$, where $b$ is the branching factor and $d$ is the solution depth. However, the most significant practical impediment to the implementation of bi-directional search often lies in the difficulty of efficiently computing the ________ operation.

predecessor Signup and view all the answers

Match the following search strategies with their properties regarding completeness and optimality in a general graph search:

Breadth-First Search (BFS) = Complete if branching factor is finite; optimal if path cost is a non-decreasing function of depth. Depth-First Search (DFS) = Not complete in infinite spaces; not optimal. Depth-Limited Search (DLS) = Complete if solution is within depth limit; not optimal. Bi-Directional Search = Complete if both searches meet; optimal if both searches use BFS. Signup and view all the answers

Consider a scenario where a robot must navigate through a complex, partially observable environment to reach a target location. Which of the following search strategies would be most appropriate if the robot has limited memory and must operate in real-time?

Real-time A* (RTA*) (D) Signup and view all the answers

In the context of solving time/exam table scheduling problems using search algorithms, which of the following constraint satisfaction techniques is most likely to yield the most efficient solution, assuming a large number of students, courses, and limited time slots?

Min-conflicts algorithm with random restarts (A) Signup and view all the answers

In a search problem with a finite state space and a known optimal solution, a search strategy that is complete but not optimal is generally preferable to one that is neither complete nor optimal.

False (B) Signup and view all the answers

Given a tree search space with a uniform branching factor of $b$ and a solution at depth $d$, derive the asymptotic space complexity for Iterative Deepening Depth-First Search (IDDFS). Explain, in detail, the rationale behind this complexity.

The asymptotic space complexity for IDDFS is $O(bd)$. Rationale: IDDFS performs a series of depth-limited depth-first searches, each with increasing depth limits. Although it repeats the initial portions of the search tree multiple times, it only needs to store the nodes along the current path from the root to the current node being explored in memory, similar to standard DFS. Since the maximum depth of exploration is limited by the current depth limit (d), and each node expands into b children, the space required to store the path is proportional to $b*d$. Thus, the space complexity remains linear with respect to the depth. Signup and view all the answers

Consider a search space where multiple goal states exist at varying depths. Under what precise condition would Depth-First Search (DFS) provably outperform Breadth-First Search (BFS) in terms of time complexity, assuming both algorithms are implemented optimally and without considering any heuristic guidance?

When all goal states are clustered within a narrowly defined subtree that is explored early in the DFS traversal due to optimal node ordering. (C) Signup and view all the answers

Given a search problem with a finite but astronomically large state space and a guarantee that a solution exists, Breadth-First Search (BFS) will invariably locate the optimal (shortest path) solution faster than Depth-First Search (DFS), assuming no additional domain-specific knowledge is available to guide either search.

False (B) Signup and view all the answers

In a scenario where memory is severely constrained and the solution depth is unknown, what iterative deepening search algorithm combines the space efficiency of Depth-First Search (DFS) with the completeness of Breadth-First Search (BFS)?

Iterative Deepening Depth-First Search (IDDFS) Signup and view all the answers

Unlike Breadth-First Search (BFS), Depth-First Search (DFS) utilizes a ______ data structure embodying a Last-In-First-Out (LIFO) principle to manage node expansion.

stack Signup and view all the answers

Match the following search algorithm characteristics with their potential consequences in pathfinding scenarios:

Breadth-First Search (BFS) = Guarantees finding the shortest path but may require substantial memory resources. Depth-First Search (DFS) = May find a solution quickly if lucky, but is not guaranteed to find the shortest path and can get lost in infinite paths. Iterative Deepening Depth-First Search (IDDFS) = Combines the memory efficiency of DFS with the completeness of BFS, but may revisit the same nodes multiple times. Uninformed Search Algorithms = Lacking domain-specific knowledge, these algorithms rely on brute-force exploration. Signup and view all the answers

Consider a state space graph where the branching factor b increases exponentially with depth d (i.e., $b(d) = e^d$). What impact does this have on the space complexity of Breadth-First Search (BFS) as a function of depth d?

The space complexity becomes exponential, $O(e^{d^2})$, reflecting the compounding effect of the branching factor. (B) Signup and view all the answers

In a finite state space with no loops or cycles and where at least one goal state guaranteed to be reachable from the initial state, Depth-First Search (DFS) is guaranteed to be both complete and optimal.

False (B) Signup and view all the answers

Describe a scenario where a queue data structure is more appropriate than a stack data structure to solve a real-world organizational problem. Provide specific details about the nature of the problem itself, and justify how a queue's attributes lead to a more effective solution than would be achieved using a stack.

Managing customer service requests where requests must be addressed in the order they arrived to ensure fairness and prevent priority inversions, utilizing the queue's FIFO structure. Signup and view all the answers

Given a uniform cost search on a graph with edges of non-uniform positive costs, the algorithm expands nodes in order of increasing ______ from the start node.

path cost Signup and view all the answers

In a massively parallel computing architecture where available memory per processing node is severely restricted, which search strategy is generally more amenable to distribution across multiple nodes to solve a large state space problem?

Depth-First Search (DFS), as it maintains only a single path in memory, minimizing the memory footprint per node. (B) Signup and view all the answers

Consider a search space represented by a tree. Assuming `b` represents the branching factor, `m` the maximum tree depth, and `d` the depth of the shallowest solution, under what conditions does breadth-first search (BFS) guarantee finding an optimal solution in terms of path cost?

When all path costs are identical, ensuring the first solution found is at depth <code>d</code>. (D) Signup and view all the answers

In a tree search algorithm, if a node is both a leaf node (i.e., has no children) and not a goal state, then it must be removed from the search agenda (queue or stack) to prevent infinite loops and ensure computational efficiency.

True (A) Signup and view all the answers

Explain how the order of node expansion in breadth-first search affects its memory requirements, particularly in search spaces with large branching factors and depth.

BFS expands nodes level by level, storing all nodes at each level in memory, leading to exponential memory consumption with respect to depth and branching factor. Signup and view all the answers

In tree search algorithms, the term _______ refers to the number of children a node possesses, profoundly impacting both time and space complexity.

branching factor Signup and view all the answers

Match the search parameters with their descriptions:

b = Branching factor: The maximum number of children any node can have. m = Maximum tree depth: The longest possible path from the root to a leaf node. d = Solution depth: The depth of the shallowest goal node in the tree. l = Search depth limit: The maximum depth to which the search algorithm explores. Signup and view all the answers

Given a search tree where the branching factor `b = 5` and the solution depth `d = 3`, what is the maximum number of nodes that breadth-first search (BFS) could potentially expand before finding the solution, assuming the root node is at depth 0?

3905 (D) Signup and view all the answers

In the context of search algorithms, which statement best characterizes the trade-off between space complexity and optimality guarantees when comparing Breadth-First Search (BFS) and Depth-First Search (DFS) in very large, potentially infinite search spaces?

BFS offers optimality guarantees at the cost of higher space complexity, while DFS sacrifices optimality to achieve lower space complexity. (A) Signup and view all the answers

If Breadth-First Search (BFS) is modified to prioritize nodes based on a heuristic function estimating the distance to the goal, it remains guaranteed to find the optimal solution, provided the heuristic is admissible.

False (B) Signup and view all the answers

Consider a scenario where the search space is a balanced binary tree of depth ‘m,’ but the solution lies at depth ‘m/2.’ Contrast the performance of Breadth-First Search (BFS) and Depth-First Search (DFS) in terms of both time and space complexity, and explain which algorithm would be more suitable for this specific problem.

BFS would be more suitable; its time complexity is $O(2^{m/2})$ and space complexity is $O(2^{m/2})$. DFS has time complexity $O(2^m)$ but space complexity $O(m)$, making BFS more efficient given the shallow solution depth. Signup and view all the answers

Consider a search problem represented as a tree with branching factor 'b' and maximum depth 'm'. A solution exists at depth 'd', where d < m. Which of the following statements accurately compares the worst-case space complexity of Breadth-First Search (BFS) and Depth-Limited Search (DLS) with depth limit 'l', where l = d?

BFS has a space complexity of O(b^d), while DLS has a space complexity of O(d), making DLS more space-efficient when the branching factor is large. (B) Signup and view all the answers

Flashcards

Search in AI

A powerful AI approach systematically exploring alternatives to find the sequence of steps towards a solution.

Uninformed Search

Search strategies that do not use any domain knowledge (Blind, naïve, Brute force).

Informed Search

A problem-solving strategy that uses domain knowledge to guide the search (Guided with heuristics, Optimal).

State Space

The set of all possible configurations of the problem, described by an initial state and possible actions.