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D 1 d 3 3 8 5 Path from a to e: Cost: 4 b 20 4 S d[v] Vertex Previous (V) (л[V]) Cost from source (d[v])

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

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Dijkstra's single-source shortest-path algorithm returns a results grid that contains the lengths of the shortest paths from a given vertex to the other vertices reachable from it. Develop a pseudocode algorithm that uses the results grid to build and return the actual path, as a list of vertices, from the source vertex to a given vertex. (Hint: This algorithm starts with a given vertex in the grid's first column and gathers ancestor vertices, until the source vertex is reached.)
"Dijkstra's single-source shortest path algorithm returns a results grid that contains the lengths of the shortest paths from a given vertex [the source vertex] to the other vertices reachable from it. Develop a pseudocode algorithm that uses the results grid to build and return the actual [shortest] path, as a list of vertices, from the source vertex to a given [target] vertex. (Hint: This algorithm starts with a given vertex [the target vertex] in the grid's first column and gathers ancestor [parent] vertices, until the source vertex is reached.)" *For your algorithm, assume that grid is the name of the results grid produced by Dijkstra's single-source shortest path algorithm. *Each vertex is identified by its label/name, which is in column 1 of grid. *As the first step of your algorithm, find the name of the source vertex. *Next, get the name of the target vertex from the user. Pseudocode should avoid details through broad-stroke statements. However, it must give enough information…
Enhance the Python-coded Luby MIS algorithm by randomly choosing a vertex, determining its neighbours, and then identifying the vertex with the lowest assigned random value to be used in the MIS.
Answer these questions please 1) Which of the following does NOT describe a step in Dijkstra's algorithm? Select one: a. Start at the ending vertex and mark it with a 0 and label it as your current vertex by putting a circle around it. b. Once you've marked all of the vertices that are connected by an edge to your current vertex, label the current vertex as visited and put an X through it. c. Always replace a vertex's mark with the new calculated distance (even if it is larger than a previous mark). d. Identify all of the vertices that are connected by an edge to your current vertex, and calculate their distance to the ending vertex by adding their current mark to the weight of the connecting edge. 2)Time Complexity of DFS is? (V - number of vertices, E - number of edges) Select one: a. 0(V + E) b. 0(V*E) c. 0(V) d. 0(E) 3)If an optimal solution can be created for a problem by constructing optimal solutions for its subproblems, the problem possesses...........property. Select…
By randomly selecting a vertex, identifying its neighbours, and then determining the vertex with the lowest assigned random value to be included in the MIS, Luby's Python-coded MIS algorithm can be improved.
Given Prim's pseudocode algorithm used as voraz algorithm (Figure 1) Where (pi) are the ancestors of the vertex in question and Q are the vertices that can be considered for expansion. Find the minimum generation tree for the graph in Figure 2 To carry out the exercise, the data structure shown in the second Table will be used. (First Table: PRIM data structure) Vertex a b c d e f g h i weight 0 inf. inf. inf. inf. inf. inf. inf. inf. pi null null null null null null null null null Q X X X X X X X X X * inf. = infinity symbol In an initial stage, the vertex a is selected and therefore we start with a weight of 0. Then, the neighbors are updated (for example, the neighbors of a are b and h). They will only be updated if the update is a lower weight than an already known one. For example, from vertex a it expands to vertex b and h leaving the table as shown below: (Second Table: First iteration) Vertex a b c d e f g h i weight 0 4 inf. inf. inf. inf. inf. 8 inf. pi…
Given PRIM's pseudocode algorithm used as voraz algorithm (Figure 1) Where (pi) are the ancestors of the vertex in question and Q are the vertices that can be considered for expansion. Find the minimum generation tree for the graph in Figure 2 To carry out the exercise, the data structure shown in the second Table will be used. (First Table: PRIM data structure) Vertex a b c d e f g h i weight 0 inf. inf. inf. inf. inf. inf. inf. inf. pi null null null null null null null null null Q X X X X X X X X X * inf. = infinity symbol In an initial stage, the vertex a is selected and therefore we start with a weight of 0. Then, the neighbors are updated (for example, the neighbors of a are b and h). They will only be updated if the update is a lower weight than an already known one. For example, from vertex a it expands to vertex b and h leaving the table as shown below: (Second Table: First iteration) Vertex a b c d e f g h i weight 0 4 inf. inf. inf. inf. inf. 8 inf. pi…
Data Structures Weighted Graph Applications Demonstration Look at Figure 29.23 which illustrates a weighted graph with 6 verticies and 8 weighted edges. Simply provide: Minimal Spanning Tree as an illustration or a textual list of edges (in our standard vertex order). Single-Source Shortest Path route from vertex 0 to the other 5 (described as one path/route for each). You may draw the two solutions and attach the illustration or describe them in text (a list of edges for the one and the vertex to vertex path the other). Be sure the final trees or path lists are clearly visible in your solution.
Luby’s Algorithm: 1. Input: G = (V, E)2. Output: MIS I of G3. I ← ∅4. V ← V5. while V = ∅6. assign a random number r(v) to each vertex v ∈ V7. for all v ∈ V in parallel8. if r(v) is minimum amongst all neighbors9. I ← I ∪ {v}10. V ← V \ {v ∪ N(v)}Make Implementation of this algorithm in sequential form in Python
Single source shortest path Algorithm1. Implement the algorithm2. Write comments3. Screenshot of output==============================================================/// Single source shortest path#include <stdio.h>#define INFINITY 9999void SingleSource(int graph[50][50], int qv, int start_ver);void main(){ int graph[50][50],qv, start_ver; int i,j; printf("\nEnter the quantity of vertexes:"); scanf("%d", &qv); printf("\nEnter the values for path costs matrix:\n"); for(i=0; i< qv; i++) for(j=0; j<qv; j++) scanf("%d", &graph[i][j]); printf("\nEnter the starting vertex:"); scanf("%d",&start_ver); SingleSource(graph, qv, start_ver); printf("\n\n\n"); return 0;}void SingleSource(int graph[50][50], int qv, int start_ver){ int eadgecost[50][50]; int distance[20]; int gen[50]; int visited[50]; int i,j; for(i=0; i<qv; i++) for(j=0; j<qv; j++) if (graph[i][j]==0) /// inserted single "="…
modify this code to find the required output; graph={ 1: [2,3], 2: [1,3], 3: [1,2,5, 4], 4: [6,11,3,5], 5: [7,4,3], 6: [8,4], 7: [5,9], 8: [6], 9: [7,10], 10: [9,12], 11: [12,4], 12: [10,11] } #perform depth-first search def dfs(graph, start, visited, charge): #current node as visited visited.add(start) #Check the Roomba needs to enter the charging station if charge <= 6: print(f" {start} (Charging, {charge} Wh) -> ") charge =12 else: print(f"{start} (Cleaning, {charge} Wh) ->") charge -= 1 #Take he list of adjacent nodes adj_nodes = graph[start] #Visit the unvisited adjacent nodes for node in adj_nodes: if node not in visited: dfs(graph, node, visited, charge) #user to enter the starting node start_node = int(input ("Enter starting node: ")) # Perform depth-first search starting from the starting node visited = set() dfs(graph, start_node, visited, 12) # Sample outputEnter starting node: 11 (Cleaning, 12 Wh) ->2…
Single source shortest path Algorithm 1. Implement the algorithm2. Write comments3. Screenshot of output /// Single source shortest path#include <stdio.h>#define INFINITY 9999void SingleSource(int graph[50][50], int qv, int start_ver);void main(){ int graph[50][50],qv, start_ver; int i,j; printf("\nEnter the quantity of vertexes:"); scanf("%d", &qv); printf("\nEnter the values for path costs matrix:\n"); for(i=0; i< qv; i++) for(j=0; j<qv; j++) scanf("%d", &graph[i][j]); printf("\nEnter the starting vertex:"); scanf("%d",&start_ver); SingleSource(graph, qv, start_ver); printf("\n\n\n"); return 0;}void SingleSource(int graph[50][50], int qv, int start_ver){ int eadgecost[50][50]; int distance[20]; int gen[50]; int visited[50]; int i,j; for(i=0; i<qv; i++) for(j=0; j<qv; j++) if (graph[i][j]==0) /// inserted single "=" instead of "=="…