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Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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Question 4: Suppose you had a road network represented as a connected graph (vertices are intersections and edges are roads between intersections). How can you determine if closing a set of intersections results in the inability to travel between some remaining pair of intersections? Note: If an intersection is closed, all edges touching that vertex are closed too. You may assume we already know about depth first search, breadth first search, minimum spanning tree algorithms, and the shortest path
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- Attached is the pseudocode for Boruvka's algorithm. What is a counterexample that shows this algorithm does not work? Draw out the graph of this counterexample and explain why the algorithm would be unable to compute an MST with your example.arrow_forwardGiven N cities represented as vertices V₁, V2, un on an undirected graph (i.e., each edge can be traversed in both directions). The graph is fully-connected where the edge eij connecting any two vertices vį and vj is the straight-line distance between these two cities. We want to search for the shortest path from v₁ (the source) to VN (the destination). ... Assume that all edges have different values, and €₁,7 has the largest value among the edges. That is, the source and destination have the largest straight-line distance. Compare the lists of explored vertices when we run the uniform-cost search and the A* search for this problem. Hint: The straight-line distance is the shortest path between any two cities. If you do not know how to start, try to run the algorithms by hand on some small cases first; but remember to make sure your graphs satisfy the conditions in the question.arrow_forwardMark Zuckerberg, the CEO of Facebook, has hired you to lead the Facebook Algorithms Group. He has asked you to use various graph algorithms to analyze the world's largest social network. The Facebook Graph has 2.8 billion vertices, with each vertex being a Facebook user. Two vertices are connected provided those two users are "friends". The first decision you need to make is how you want to model the Facebook graph. Determine whether you should use an adjacency-list representation or an adjacency-matrix representation.arrow_forward
- Given N cities represented as vertices V₁, V2,..., UN on an undirected graph (i.e., each edge can be traversed in both directions). The graph is fully-connected where the edge eij connecting any two vertices v; and vj is the straight-line distance between these two cities. We want to search for the shortest path from v₁ (the source) to VN (the destination). Assume that all edges have different values, and e₁, has the largest value among the edges. That is, the source and destination have the largest straight-line distance. Compare the lists of explored vertices when we run the uniform-cost search and the A* search for this problem. Hint: The straight-line distance is the shortest path between any two cities. If you do not know how to start, try to run the algorithms by hand on some small cases first; but remember to make sure your graphs satisfy the conditions in the question.arrow_forwardThere are many applications of Shortest Path Algorithm. Consider the problem of solving a jumbled Rubik's Cube in the fewest number of moves. I claim that this problem can be solved using a Shortest Path Algorithm. Determine whether this statement is TRUE or FALSE. NOTE: if you want to check if this statement is TRUE, think about how the Rubik's Cube Problem can be represented as a graph. What are the vertices? Which pairs of vertices are connected with edges? What is your source vertex and what is your destination vertex? How would Dijkstra's Algorithm enable you to find the optimal sequence of moves to solve a jumbled cube in the fewest number of moves?arrow_forwardExercise 12.9 Given a weighted (connected) undirected graph G = (V, E, w), with m =n+ 0(1) edges (i.e., the number of edges is at most the number of vertices plus some constant), give an O(n)-time algorithm to compute the minimum spanning tree of G. Prove the correctness and the running time of your algorithm. (Hint: Think of how one can eliminate an edge from being in the MST.)arrow_forward
- Show what the final distance and previous array values will be after running the shortest path algorithm from class on the following graph, starting at vertex 2: 1 6 5 4 4 4 2 7 0 5 5 6 2 2 3 13 6arrow_forwardJava Pleasse add Comments and Test-Cases to code. explore a specific way to perform a Breadth First Search (BFS) of a given Graph [ Figure 1].arrow_forwardJava. Please use the template in the picture, thank you!arrow_forward
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