Artificial Intelligence: A Modern Approach
3rd Edition
ISBN: 9780136042594
Author: Stuart Russell, Peter Norvig
Publisher: Prentice Hall
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Chapter 3, Problem 14E
Explanation of Solution
a. Depth-first search always expands at least as many nodes as A* search with an admissible heuristic:
- It is a false statement.
- Reason: a lucky DFS might expand exactly d nodes in order to reach the goal.
- A* largely dominates any graph-search
algorithm that is guaranteed to find optimal solutions.
b. h(n)=0 is an admissible heuristic for the 8-puzzle.
- It is a true statement
- Reason: h(n)=0 is always an admissible heuristic, since costs are nonnegative.
c. A* is of no use in robotics because percepts, states, actions are continuous.
- It is a true statement.
- Reason: A*search is generally used in robotics...
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Students have asked these similar questions
Artificial Intelligence - Adversarial Search
1. Consider the following three variants of minimax search: the simple version, alpha-beta search, anddepth-limited search, and consider the games of tic-tac-toe and chess. For the chess game, supposethat the Threefold Repetition Rule and the Fifty-Move Rule, and the similar rules if any, are notconsidered, i.e., the game will not terminate if the same position occurs multiple times. For eachcombination of minimax variant and game, answer the following question: can that minimax variantpossibly never terminate, in computing the best next move? Justify your answer.
Consider a graph and implement Breadth-first search, Uniform-cost search, Depth-first search, Depth-limited search, Iterative deepening depth-first search and Bidirectional search using your favorite programming language. Also draw and visualize the solution.
3) The graph k-coloring problem is stated as follows: Given an undirected graph G= (V,E)
with N vertices and M edges and an integer k. Assign to each vertex v in V a color c(v)
such that 1
Chapter 3 Solutions
Artificial Intelligence: A Modern Approach
Ch. 3 - Explain why problem formulation must follow goal...Ch. 3 - Prob. 2ECh. 3 - Prob. 3ECh. 3 - Prob. 4ECh. 3 - Prob. 5ECh. 3 - Prob. 6ECh. 3 - Prob. 8ECh. 3 - Prob. 9ECh. 3 - Prob. 10ECh. 3 - Prob. 11E
Ch. 3 - Prob. 12ECh. 3 - Prob. 13ECh. 3 - Prob. 14ECh. 3 - Prob. 15ECh. 3 - Prob. 16ECh. 3 - Prob. 17ECh. 3 - Prob. 18ECh. 3 - Prob. 20ECh. 3 - Prob. 21ECh. 3 - Prob. 22ECh. 3 - Trace the operation of A search applied to the...Ch. 3 - Prob. 24ECh. 3 - Prob. 25ECh. 3 - Prob. 26ECh. 3 - Prob. 27ECh. 3 - Prob. 28ECh. 3 - Prob. 29ECh. 3 - Prob. 31ECh. 3 - Prob. 32E
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- 3) The graph k-coloring problem is stated as follows: Given an undirected graph G = (V,E) with N vertices and M edges and an integer k. Assign to each vertex v in Va color c(v) such that 1< c(v)arrow_forwardTrue or False (If your answer to the question is "False", explain why, and provide correction when possible). (a) Let h(n) be the heuristics for the node n, h(m) be the heuristics for the node m, d(m,n) be the actual minimal cost from node m to n in a graph. A* satisfies the monotone restriction iff d(m,n) <= |h(n)-h(m)|. (b) If an A* heuristics is admissible then it satisfies the monotone restriction. (c) Best-first search guarantees optimality in its returned solution. (d) Least-cost-first search guarantees optimality in its returned solution. (e) If all edges are with unit cost, then Breadth-first search guarantees optimality in its returned solution.arrow_forwardDo some outside research on depth-first traversal as it relates to traversing graphs. Then answer the following questions: a. Suppose you have an arbitrary connected graph G, shown in the image below. Use the vertex A as your starting point. Write out the order in which the algorithm could traverse the graph with a depth-first search, and explain your reasoning (there are multiple correct answers, hence the need for an explanation). b. Use a proof by induction to prove that when a depth-first traversal is performed, every vertex v in your graph G will have been visited at least one time. B D H E A G с I FLarrow_forwardTrue or False (If your answer to the question is "False", explain why, and provide correction when possible). (a) Let h(n) be the heuristics for the node n, h(m) be the heuristics for the node m, d(m,n) be the actual minimal cost from node m to n in a graph. A* satisfies the monotone restriction iff d(m,n)arrow_forwardReview the 8-puzzle problem. Consider that the initial state is 1 3 48 27 6 5and the goal state is1 2 38 47 6 5Apply the breath-first-search method to obtain the path from the initial state to the goal state. Youneed to show the corresponding search tree. As soon as you find the goal state, you can stop the searchprocess.arrow_forward(V, E) be a connected, undirected graph. Let A = V, B = V, and f(u) = neighbours of u. Select all that are true. Let G = a) f: AB is not a function Ob) f: A B is a function but we cannot always apply the Pigeonhole Principle with this A, B Odf: A B is a function but we cannot always apply the extended Pigeonhole Principle with this A, B d) none of the abovearrow_forward2. An undirected graph G can be partitioned into connected components, where two nodes are in the same connected component if and only if there is a path connecting them. Design and analyze an efficient algorithm that computes the connected components of a graph G given in adjacency list format. Be sure to give a correctness argument and detailed time analysis. You can use algorithms from class as a sub-procedure, but be sure to use the claims proven about them carefully. A good algorithm has time approximately 0(n + m) where the graph has n nodes and m edges.arrow_forwardCorrect answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. society can be addressed by an associated, undirected chart of n vertices and m edges. The vertices address individuals, and an edge (i,j) addresses a companionship between individuals I and j. In the public eye, the I-th individual has a pay artificial intelligence. An individual I is desirous of individual j if aj=ai+1. That is if individual j has precisely 1 more unit of pay than individual I. The general public is called entrepreneur if for each pair of companions one is desirous of the other. For certain fellowships, you know which companion is jealous of the other. For the leftover fellowships, you don't have the foggiest idea about the bearing of jealousy. The pay imbalance of society is characterized as max1≤i≤nai−min1≤i≤nai. You just know the fellowships and not the livelihoods. In case it is outlandish for this general public to be industrialist with the given…arrow_forwarda) Given a depth-first search tree T, the set of edges in T are referred to as "tree edges" while those not in T are referred to as "back edges". Modify the implementation of the Depth-First Search algorithm to print out the set of tree edges and the set of back edges for the following graph. 1(0 1 1 0 0 1 o) 210 10 0 0 31 10 1 0 0 1 40 0 10 0 0 0 50 0 0 0 0 1 1 6 10 001 70 0 10 1 1 0 0 1arrow_forwardGiven a graph that is a tree (connected and acyclic). (I) Pick any vertex v.(II) Compute the shortest path from v to every other vertex. Let w be the vertex with the largest shortest path distance.(III) Compute the shortest path from w to every other vertex. Let x be the vertex with the largest shortest path distance. Consider the path p from w to x. Which of the following are truea. p is the longest path in the graphb. p is the shortest path in the graphc. p can be calculated in time linear in the number of edges/verticesarrow_forwardPlease Answer this in Python language: You're given a simple undirected graph G with N vertices and M edges. You have to assign, to each vertex i, a number C; such that 1 ≤ C; ≤ N and Vi‡j, C; ‡ Cj. For any such assignment, we define D; to be the number of neighbours j of i such that C; < C₁. You want to minimise maai[1..N) Di - mini[1..N) Di. Output the minimum possible value of this expression for a valid assignment as described above, and also print the corresponding assignment. Note: The given graph need not be connected. • If there are multiple possible assignments, output anyone. • Since the input is large, prefer using fast input-output methods. Input 1 57 12 13 14 23 24 25 35 Output 2 43251 Qarrow_forwardExercise d. Coloring, with the oracle's help. (Textbook problem 4.2) Analogous to the previous problem, but a little trickier: suppose we have an oracle for the decision problem GRAPH k-COLORING. Show that by asking a polynomial number of questions, we can find a k-coloring if one exists. Hint: You want to iteratively compute a coloring, where partway through, some nodes have colors assigned already and others do not. You need to ask the oracle about a modified version of the original graph to learn if this partial coloring can be finished; if not, make a different choice when coloring the next node.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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