Based on our lectures and the BELLMAN-FORD algorithm below, answer the following questions.BELLMAN-FORD (G, w, s)1INITIALIZE-SINGLE-SOURCE (G, s)2 for i = 1 to |G. VI - 1345678for each edge (u, v) = G.ERELAX(u, v, w)for each edge (u, v) = G.Eif v.d> u.d+w(u, v)return FALSEreturn TRUE1. What does the algorithm return?2. Analyze the complexity of the algorithm.

1. What does the Bellman-Ford algorithm return?The Bellman-Ford algorithm determines two…

Answered: Based on our lectures and the…

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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8. Answer the following questions for a random graph generated by the Erdos-Renyi random graph model ER(n, p). You do not need to prove your answers are correct but still need to show your work. Your answer should be in terms of n and p. 8(a) What is the expected number of triangles? 8(b) What is the probability that d(u, v) > 2 for two particular vertices u v? (Hint: First, find the probability that d(u, v) > 1. Then consider, for all other vertices x, the probability that uxv is NOT a path in the random graph. Multiply all these probabilities together.) Note that for this question, no graph is given. However, we know that the expected number of edges for ER(n, p) random graph model is , and that the expected degrees of the vertex for the random graph model ER(n, p) is (n-1) *p
In the Given graph G=(V, E), find Shortest paths among all pairs of vertices by using Floyed Warshall Algorithm. V={a, b, c, d, e} and E={(a, b, 3), (a, c, 8), (a, e, 4), (b, d, 1), (b, e, 7), (b, c, 4), (d, c, -5), (d, b, 6), (d, a, 2), (e, d, 6)}. Note: Numeric value is the weight of the corresponding edge.
Consider the following weighted undirected graph with 7 vertices and 11 edges. A C 7 В 5 9. 7 15 E D 8 6 9. 11 Apply Dijkstra's Algorithm on the graph above, to determine the shortest distance from vertex G to each of the other six vertices (A, B, C, D, E, F). Clearly show all of your steps.
For the graph below determine the minimum number of colors necessary to colorits vertices. Justify your answer, by (i) giving a coloring and (ii) explaining why it is not possibleto use fewer colors. You can represent colors by letters a, b, c, .... To show the coloring, mark eachvertex with its color.
(1) Draw a transition graph for the dfa M={ Q,E, 8.q..F), where Q={g,.g1-42}. E= {a, b}, F = {q1} and ô is defined as S(q0, a) = q1- 8(q0, b) = q0, 8(q1, b) = q1. 8(q1, a) = q2, 8(q2, b) = q2, ô(q2, a) = q2 (2) Give the language accepted by the above dfa.
Use the nearest neighbor algorithm starting at each of the indicated vertices to determine an approximate solution to the problem of finding a minimum Hamilton circuit for the graph. In each case, find the total weight of the circuit found. (a) Starting at A (b) Starting at C (c) Starting at D (d) Starting at E →□→□→□→□→ロ (a) The circuit starting at A is A→ C.. A 25 E 10. 5 35 20 30 30 B 15 D 40 20 C
Find an adjacency matrix and a graph representation for
Use A algorithm to find the solution path for the following graph where the h(n) for the states are {(S, 2), (A, 3), (B, 5), (C, 4), (D, 20), (E, 9), (F, 7), (H, 8), (G, 0)}. A 3 -5 F 6. 1. E H
MATLAB
Bellman-Ford algorithm Draw a graph G with weights of edges ranging from 3 to 9, is it possible to calculate the LONGEST PATH without altering the algorithm at all? Justify your answer by providing solid reasons.
For the graph below determine the minimum number of colors necessary to colorits vertices. Justify your answer, by (i) giving a coloring and (ii) explaining why it is not possibleto use fewer colors. You can represent colors by letters a, b, c, .... To show the coloring, mark eachvertex with its color.
For each graph representation, select the appropriate worst-case space complexity: Adjacency Matrix: Edge List : Adjacency List: o(V+E) O(E^2) O(E) O(V^2)

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