4. (15%) Use Dijkstra's algorithm to solve the SSSP problem for the following graph. Illustrate each step by marking each growing edge and labeling each vertex-v (v- (b,c,d.ef) with its updated shortest distance d(v) from the source vertex a in the circle. The first step is already shown in (a). Continue from (b). You may or may not show steps in the way as in the textbook Page 336.

4. (15%) Use Dijkstra's algorithm to solve the SSSP problem for the following graph. Illustrate each step by marking each growing edge and labeling each vertex-v (v- (b,c,d.ef) with its updated shortest distance d(v) from the source vertex a in the circle. The first step is already shown in (a). Continue from (b). You may or may not show steps in the way as in the textbook Page 336.

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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Please give an explanation as to why your answer is correct.
B Write a topological order of vertices of above graph and illustrate your method.
consider the following undirected graph.
We are given an undirected connected graph G = (V, E) and vertices s and t.Initially, there is a robot at position s and we want to move this robot to position t by moving it along theedges of the graph; at any time step, we can move the robot to one of the neighboring vertices and the robotwill reach that vertex in the next time step.However, we have a problem: at every time step, a subset of vertices of this graph undergo maintenance andif the robot is on one of these vertices at this time step, it will be destroyed (!). Luckily, we are given theschedule of the maintenance for the next T time steps in an array M [1 : T ], where each M [i] is a linked-listof the vertices that undergo maintenance at time step i.Design an algorithm that finds a route for the robot to go from s to t in at most T seconds so that at notime i, the robot is on one of the maintained vertices, or output that this is not possible. The runtime ofyour algorithm should ideally be O((n + m) ·T ) but you will…
„ Run the Dijkstra's algorithm on the following graph beginning at node S. 5 12 6 3 5 16 Problem 3-(1). After each iteration, show the D values of all nodes (initial D values are shown above each node in red). Problem 3-(2). Show the shortest path from S to every other node generated by the algorithm 8 e.
Q7: Run the Ford-Fulkerson algorithm on the graph assigned to you and determine the maximum flow possible between the source (s) and destination (d) as well as determine the minimum cut of edges (set of edges with the minimum sum of the edge weights) to disconnect the source and destination. Show all the work (including the use of the residual graphs in each iteration).
b) Apply an algorithm to find the minimum spanning tree. To solve this problem, you need to transfer the unweighted graph into weighted graph and you can do it by using your mobile number (11 digits). Just assign the digits sequentially (left to right) to the edges of binary tree segment (means black color edges). And for rest of the edges, you may write 1 as their weights.
a) Illustrate the sequence of vertices of this graph visited using depth-first search traversal starting at vertex g. b) Illustrate adjacency list representation and adjacency matrix representation, respectively, for this graph. What are the advantages and disadvantages of those two representations? c) Describe an algorithm to find in the graph a path illustrated below that goes through every edge exactly once in each direction.
3. Let G be the following graph. V1 V7 V2 V8 V5 V6 V3 V4 (a) Using the greedy algorithm, proper vertex-color G with the order V₁, V2, V3, V4, V5, V6, V7, Vg. How many colors did you use? (b) Find x(G) and show a coloring that demonstrates this. (c) Provide an ordering of the vertices that when input into the greedy algorithm, produces a proper vertex-coloring that uses x(G) many colors.
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Note: Solve the following question and please don't repost previous answers and don't give a computer generated answer. Problem: Draw a simple, connected, directed, weighted graph with 9 vertices and 17 edges, each with unique edge weights. Identify one vertex as a “start” vertex and illustrate a running of Dijkstra’s algorithm on this graph.
We have the following directed graph G, where the number on each edge is the cost of the edge. 1. Step through Dijkstra’s Algorithm on the graph starting from vertex s, and complete the table below to show what the arrays d and p are at each step of the algorithm. For any vertex x, d[x] stores the current shortest distance from s to x, and p[x] stores the current parent vertex of x. 2. After you complete the table, provide the returned shortest path from s to t and the cost of the path.