Artificial Intelligence: A Modern Approach
Artificial Intelligence: A Modern Approach
3rd Edition
ISBN: 9780136042594
Author: Stuart Russell, Peter Norvig
Publisher: Prentice Hall
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Chapter 6, Problem 17E

Explanation of Solution

Algorithm for finding minimal cycle cutest:

  • A simple algorithm for finding a cutset of no more than k nodes is to enumerate all subsets of nodes of size 1,2,...,k.
  • The user has to check whether the remaining nodes form a tree for each subset.
  • The algorithm takes   time. That is O(nk).
  • The Modified Greedy Algorithm (MGA) introduced by Becker and Geiger, finds a cutest that is twice the size of the minimal cutest...

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Provide an eficient algorithm that given a directed graph G with n vertices and m edges as input, finds the outdegree of each vertex in G. Note that outdegree of a vertex u is the number of edges directed from u to some other vertex v. Discuss the running-time of your algorithm and Provide an algorithm that given a directed graph G with n vertices and m edges as input, nds the indegree of each vertex in G. Note that indegree of a vertex u is the number of edges directed into u from some other vertex v. Discuss the running-time of your algorithm.
Consider an undirected graph with n nodes and m edges. The goal is to find a path between two specified nodes u and v that maximizes the minimum weight of any edge along the path. Assume that all edge weights are positive and distinct. Design an algorithm to solve this problem with a time complexity of O(m log n).
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