Exercise 1.Describe in plain English (a short paragraph with at most 5-6 lines should be enough)an algorithm for the following task:Input: A directed graph G = (V, E), and a node u € V.Goal: Output 1 if there is a path from every v € G to u (so if u is reachable from anyother node), and output 0 otherwise.Your algorithm should have runtime O(n + m). (Hint: Use an idea that we have seenfor similar connectivity problems in directed graphs.)

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Exercise 1. Describe in plain English (a short paragraph with at most 5-6 lines should be enough) n algorithm for the following task: Input: A directed graph G = (V, E), and a node u € V. Goal: Output 1 if there is a path from every v E G to u (so if u is reachable from any ther node), and output 0 otherwise. Your algorithm should have runtime O(n + m). (Hint: Use an idea that we have seen

Exercise 1. Describe in plain English (a short paragraph with at most 5-6 lines should be enough) n algorithm for the following task: Input: A directed graph G = (V, E), and a node u € V. Goal: Output 1 if there is a path from every v E G to u (so if u is reachable from any ther node), and output 0 otherwise. Your algorithm should have runtime O(n + m). (Hint: Use an idea that we have seen

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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Answer the following statements as true or false regarding Prim's algorithm: a. True or False: Prim's algorithm can only be used on weighted graphs. b. True or False: Prim's algorithm will produce a graph with equal number of vertices and edges
6. In Java create an algorithm for an undirected graph with n vertices and m edges that...- Takes as a parameter some integer k- Returns the maximum induced subgraph where each vertex of that subgraph has a degree greater than or equal to k (or returns null if no such subgraph exists)- Operates in O(n + m) time
9:17 Today Edit 9:17 AM Given a directed graph G=(V, E), design an algorithm to find out whether there is a route between two nodes, say, u and v. Your design should be based on depth first search and should be given in pseudo code.
*Discrete Math In the graph above, let ε = {2, 3}, Let G−ε be the graph that is obtained from G by deleting the edge {2,3}. Let G∗ be the graph that is obtain from G − ε by merging 2 and 3 into a single vertex w. (As in the notes, v is adjacent to w in the new if and only if either {2,v} or {3,v is an edge of G.) (a) Draw G − ε and calculate its chromatic polynomial. (b) Give an example of a vertex coloring that is proper for G − ε, but not for G. (c) Explain, in own words, why no coloring can be proper for G but not proper for G − ε. (d) Draw G∗ and calculate its chromatic polynomial. (e) Verify that, for this example,PG(k) = PG−ε(k) − PG∗ (k).
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).
Code this In python 13. Describe and analyze an algorithm to determine the number of shortest paths from a source vertex s to a target vertex t in an arbitrary directed graph G with weighted edges. You may assume that all edge weights are positive and that all necessary arithmetic operations can be performed in Exercises 0(1) time. [Hint: Compute shortest path distances from s to every other vertex. Throw away all edges that cannot be part of a shortest path from s to another vertex. What's left?]
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a) write the algorithm b) Briefly explain why the algorithm solves the problem, and the correctness c ) State and briefly explain the running time of your algorithm
Use of Matching for Edge ColouringEdges in a matching can share the same colour since matching in a graph is defined as the collection of non-adjacent edges. As a result, we can create an algorithm based on this idea using the below stages. 1. Input: G = (V, E)2. Output: Minimal edge coloring of G3. color ← 04. while G = ∅$5. find maximal matching M of G6. color all M vertices with color7. G ← G − M8. color ← color + 1implementation of Python
Alert dont submit AI generated answer. Write a program that reads a weighted graph and an initial vertex.The program must print on the screen the minimum paths obtained by Dijkstra's algorithm. Input: Receives n, m and s; n is the total number of vertices, m the total number of arcs and s is the initial vertex.Next, m lines, each line with a trio of integers, corresponding to the beginning and end of the arc, followed by the weight of the arc.(Vertices are identified from 0 to n-1.) Output: Prints the shortest paths obtained by Dijkstra's algorithm. Exemple: Input: 5 10 00 1 100 4 51 2 11 4 22 3 43 2 63 0 74 1 34 2 94 3 2 Output: [0, 8, 9, 7, 5][-1, 4, 1, 4, 0]
Question 1.Implement a computer program in C to compute the shortest path between two nominated vertices on the graph,G, using Dijkstra’s algorithm.InstructionsGiven a picture of an arbitrary undirected, simple, weighted graph, G, with a maximum of 10 vertices:a. Capture the graph, G=(V, E), into your program;b. Nominate an initial vertex and a goal vertex;c. Calculate the shortest path between those two vertices;d. Display the shortest route between the two vertices;e. Display the distance or cost of the route. The following discussion points should be included: Description of graph capture method Implementation choices Screenshot of program output Relevant example or use in practice Reflection Hints Make use of the graph test case provided to verify that your implementation is operating correctly See the extra FAQ document for additional clarification on common questions See section 6.3.1 Skiena 2nd edition and section 8.31 Skiena 3rd edition There are numerous ways to…
1. This question is about type of graphs. a. Construct a graph with exactly 5 nodes such that the graph is strongly connected. b. Construct a graph with exactly 5 nodes such that the graph is weakly connected. c. Construct a graph with exactly 5 nodes such that the graph is completely connected. d. Construct a graph with exactly 5 nodes such that the graph is not connected. e. Construct a graph with exactly 5 nodes such that the graph is not a simple graph.