1. Given the map below, we want to find a path from K to R. Consider only graph search, i.e each state is visited at most once in the search process. For equally preferred nodes, generate and expand them in alphabetical order. (a) List the states expanded, in the correct order, if we use breadth-first search (BFS). What is the solution path? (b) List the states expanded, in the correct order, if we use uniform-cost search. What is the solution path? (c) Show the process of A* search with the straight-line distance as heuristic. What is the solution path?

1. Given the map below, we want to find a path from K to R. Consider only graph search, i.e each state is visited at most once in the search process. For equally preferred nodes, generate and expand them in alphabetical order. (a) List the states expanded, in the correct order, if we use breadth-first search (BFS). What is the solution path? (b) List the states expanded, in the correct order, if we use uniform-cost search. What is the solution path? (c) Show the process of A* search with the straight-line distance as heuristic. What is the solution path?

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Similar questions

PROBLEM 2. Let G be an undirected graph whose vertices are the integers 1 through 8, and let the adjacent vertices of each vertex be given by the table below: Assume that, in a traversal of G, the adjacent vertices of a given vertex are returned in the same order as they are listed in the table above.a. Draw G.b. Give the sequence of vertices of G visited using a DFS traversal starting at vertex 1.c. Give the sequence of vertices visited using a BFS traversal starting at vertex 1.
Q1) how many graphs are there on 20 nodes? (To make this question precise, we have to make sure we known what it mean that two graphs are the same . For the purpose of this exercise,we consider the nodes given and labeled,say,asAlice ,Bob,...... The graph consisting of a single edge connecting Alice and Bob is different from the graph consisting of a single edge connecting Eve and frank.) Q2) Formulate the following assertion as a theorem about graphs and prove it :At every party one can find two people who know the same number of other people (like Bob and Eve in our first example).
Is the following statement true or false? a. Performing one rotation always preserves the AVL property. b. For any two functions f and g, we always have either f = O(g) or g = O(f). c. We run the breadth-first search algorithm (BFS) on a undirected graph G such that all edges have the same weight. BFS returns the shortest path from a source vertex s to any other vertex.
Consider the navigation problem shown in Figure 1. The number next to each edge is the cost of the performing the action corresponding to that edge. You start from A and your goal is to get to F. List the order in which nodes are expanded, which nodes are added to the fringe and which states are added to the closed set when performing Graph Search using: breadth-first search. depth-first search. iterative deepening search. uniform cost search
Consider a graph G in the following Find a path from a to g in the graph G using each search strategy of depth-first search, breadth-first search, least-cost search, best-first search, and A* search. Is the returned solution path an optimal one?
please answer both of the questions. 7. The Bellman-Ford algorithm for single-source shortest paths on a graph G(V,E) as discussed in class has a running time of O|V |3, where |V | is the number of vertices in the given graph. However, when the graph is sparse (i.e., |E| << |V |2), then this running time can be improved to O(|V ||E|). Describe how how this can be done.. 8. Let G(V,E) be an undirected graph such that each vertex has an even degree. Design an O(|V |+ |E|) time algorithm to direct the edges of G such that, for each vertex, the outdegree is equal to the indegree. Please give proper explanation and typed answer only.
For the undirected graph G shown in Exampleand reproduced here for convenience, undertake Breadth first search for the key 9, by refining the Breadth first traversal algorithm.
explain a graph problem that has a direct and efficient algorithm using breadth first search, but whose solution is not nearly so straight forward if the algorithm was based on depth first search.
Apply the Breadth first traversal algorithm to the undirected graph G given in Example and replicated here for convenience. The goal is to do a Breadth first search for the key 9.
Answer True or False to the following claims: a. If G is graph on at most 5 vertices and every vertex has degree 2, then G is a cycle. b. Let G be a forest. If we add an edge to G, then G is no longer a forest. c. Let G be a graph, and let u, v, and w be vertices in G. Suppose that a shortest path from u to v in G is of length 3, andsuppose that a shortest path from v to w in G is of length 4. Then a shortest path from u to w in G is of length 7.
You are given a graph G = (V, E) with positive edge weights, and a minimum spanning tree T = (V, E') with respect to these weights; you may assume G and T are given as adjacency lists. Now suppose the weight of a particular edge e in E is modified from w(e) to a new value w̃(e). You wish to quickly update the minimum spanning tree T to reflect this change, without recomputing the entire tree from scratch. There are four cases. In each case give a linear-time algorithm for updating the tree. Note, you are given the tree T and the edge e = (y, z) whose weight is changed; you are told its old weight w(e) and its new weight w~(e) (which you type in latex by widetilde{w}(e) surrounded by double dollar signs). In each case specify if the tree might change. And if it might change then give an algorithm to find the weight of the possibly new MST (just return the weight or the MST, whatever's easier). You can use the algorithms DFS, Explore, BFS, Dijkstra's, SCC, Topological Sort as…
how could someone solce this one? The Chinese postman problem: Consider an undirected connected graph and a given starting node. The Chinese postman has to find the shortest route through the graph that starts and ends in the starting node such that all links are passed. The same problem appears for instance for snow cleaning or garbage collection in a city. For a branch-and-bound algorithm, find a possible lower bound function. (Remark: If the problem is to pass through all nodes of the graph, it is called the travelling salesman problem - which needs different solution algorithms, but also of the branch-and-bound type).).