Artificial Intelligence: A Modern Approach
Artificial Intelligence: A Modern Approach
3rd Edition
ISBN: 9780136042594
Author: Stuart Russell, Peter Norvig
Publisher: Prentice Hall
Expert Solution & Answer
Book Icon
Chapter 3, Problem 17E

Explanation of Solution

a.

Illustration of iterative lengthening search algorithm is optimal for the general path costs:

  • Uniform cost just iteratively inspects the unexplored node nearest to the start node.
  • Iterative lengthening search is a uniform cost search that runs multiple times with a growing cost limit from start to finish.
  • The iterative lengthening search has not that much advantage as the iterative deepening search possesses.
  • The weakness of iterative lengthening search:
    • The algorithm simply searches the same node each time and adds more at the ends than the nearest first node and the next closest node are invariant...

Explanation of Solution

b.

Number of iterations required for iterative deepening:

  • The uniform cost search will run through the nodes in the same order as that of the first breadth search.
  • The search progression will go as follows,
    • Assume that the goal node is found halfway through the search operation of depth, on average.
    • Thus the goal iteration = “b+b2+...+bd/2

Explanation of Solution

c.

Number of iterations required in the worst case:

In the worst case, the limit begins at “0” and increments by a minimum positive cost “ε”, until it reaches the value “d”

Explanation of Solution

d.

Performance of algorithm compared to uniform cost search algorithm:

  • The algorithm requires only “k” uniform cost searches where iteration simply expands the boundary for the closest nodes inspected...

Blurred answer
Students have asked these similar questions
Please answer the following question in detail and explain all the proofs and assumptions for all parts. The question has three parts, (a), (b) and (c).   Iterative lengthening search is an iterative analogue of uniform-cost search. The basic idea is to use increasing limits on path cost. If a node is generated whose path cost exceeds the current limit, it is immediately discarded. For each new iteration, the limit is set to the lowest path cost of any node discarded in the previous iteration. (a) Show that this algorithm is optimal for general path costs. You may assume that all costs are integers (this is not a loss of generality if the search space is finite). You may wish to consider the minimal path cost C; what happens when we set the path cost to be some limit l < C? (b) Consider a uniform tree with branching factor b, solution depth d, and unit step costs (each action costs one unit). How many iterations will iterative lengthening require? (c) (7 points) Now consider the…
We know that when we have a graph with negative edge costs, Dijkstra’s algorithm is not guaranteed to work.   (a) Does Dijkstra’s algorithm ever work when some of the edge costs are negative? Explain why or why not.   (b) Find an algorithm that will always find a shortest path between two nodes, under the assumption that at most one edge in the input has a negative weight. Your algorithm should run in time O(m log n), where m is the number of edges and n is the number of nodes. That is, the runnning time should be at most a constant factor slower than Dijkstra’s algorithm. To be clear, your algorithm takes as input   (i) a directed graph, G, given in adjacency list form. (ii) a weight function f, which, given two adjacent nodes, v,w, returns the weight of the edge between them. For non-adjacent nodes v,w, you may assume f(v,w) returns +1. (iii) a pair of nodes, s, t. If the input contains a negative cycle, you should find one and output it. Otherwise, if the graph contains at least one…
Write the algorithm that finds and returns how many paths in k units of length between any given two nodes (source node, destination node; source and target nodes can also be the same) in a non-directional and unweighted line of N nodes represented as a neighborhood matrix. (Assume that each side in the unweighted diagram is one unit long.) Note: By using the problem reduction method of the Transform and Conquer strategy, you have to make the given problem into another problem. Algorithm howManyPath (M [0..N-1] [0..N-1], source, target, k)// Input: NxN neighborhood matrix, source, target nodes, k value.// Ouput: In the given line, there are how many different paths of k units length between the given source and target node.
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Database System Concepts
Computer Science
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:McGraw-Hill Education
Text book image
Starting Out with Python (4th Edition)
Computer Science
ISBN:9780134444321
Author:Tony Gaddis
Publisher:PEARSON
Text book image
Digital Fundamentals (11th Edition)
Computer Science
ISBN:9780132737968
Author:Thomas L. Floyd
Publisher:PEARSON
Text book image
C How to Program (8th Edition)
Computer Science
ISBN:9780133976892
Author:Paul J. Deitel, Harvey Deitel
Publisher:PEARSON
Text book image
Database Systems: Design, Implementation, & Manag...
Computer Science
ISBN:9781337627900
Author:Carlos Coronel, Steven Morris
Publisher:Cengage Learning
Text book image
Programmable Logic Controllers
Computer Science
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education