(ii) (iii) (a) Figure 3.0 shows an undirected weighted graph A. C 2 B 3 3 E 2 H A 2 2 G I F 3 Figure 3.0 Undirected Weighted Graph A Starting at vertex C, traverse the graph by using Depth-First-Search (DFS). The vertices are to be traversed alphabetically. Give the order in which the vertices are traversed. Starting at vertex C, traverse the graph by using Breadth-First-Search (BFS). The vertices are to be traversed alphabetically. Give the order in which the vertices are traversed.

(ii) (iii) (a) Figure 3.0 shows an undirected weighted graph A. C 2 B 3 3 E 2 H A 2 2 G I F 3 Figure 3.0 Undirected Weighted Graph A Starting at vertex C, traverse the graph by using Depth-First-Search (DFS). The vertices are to be traversed alphabetically. Give the order in which the vertices are traversed. Starting at vertex C, traverse the graph by using Breadth-First-Search (BFS). The vertices are to be traversed alphabetically. Give the order in which the vertices are traversed.

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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(1) T F Given a directed graph G and a vertex v in the graph, breath first search (BFS) can be used to detect if v is part of a cycle in the graph. (2) T F Let P be a shortest path from some vertex s to some other vertex t in a directed graph. If the weight of each edge in the graph is decreased by one, then P will still be a shortest path from s to t. (3) T F edge Kruskal's algorithm is always correct even in graphs with negative weights. (4) T F For any flow network, there is only one unique way to assign flow value to the edges so as to achieve the maximum flow for the network. NP problems are those problems that cannot be solved in polynomial (5) T F time.
Computer Science: Data Structures and Algorithm (C Programming) A strongly connected component (SCC) of a directed graph G(V,E) is a maximal set of vertices C⊆V suchthatforeverypairofverticesuandvinC,wehavebothu↝vandv↝u;that is, vertices u and v are reachable from each other.In the example graph given below, the sets of nodes a, b, e, c, d, f, g, and h each form a strongly connected component. Thus, the graph consists of 4 strongly connected components. (a) Breadth First Search (BFS) can be used in determining whether each node in a given directed graph is reachable by every other node. Give the pseudocode of an algorithm using BFS that determines whether a given directed graph is a single SCC. Also provide the explanation of your algorithm in plain English along with a runtime analysis. (b) Depth First Search (DFS) can be used to calculate strongly connected compo- nents in a graph. Give the pseudocode of an algorithm using DFS that calculates SCCs in a given directed graph. Also…
(9) An undirected weighted graph G is given below: a d 5 2 3 6 لها b 8 5 7 e 1 4 3 с 6 3 4 f 4 4 h 2 8 Use Prim's algorithm to compute the minimum spanning tree for the weighted graph. Start the algorithm at vertex a.
Specifications: You will create an implementation of this algorithm. Your driver program should provide a graph and a source vertex in the graph. Your implementation should use Dijkstra's Algorithm to determine the shortest path using adjacency matrix representation. Specifically, given a graph and a source vertex in the graph, find the shortest paths from source to all vertices in the given graph, using Dijkstra's Algorithm.
2. [20 points][MID] The graph k-coloring problem is stated as follows: Given an undirected graph G = (V, E) with N vertices and M edges and an integer k. Assign to each vertex v in V a color e(r) such that 1 < e{u) < k and c(u) # c(v) for every edge (u, v) in E. In other words you want to color each vertex with one of the k colors you have and no two adjacent vertices can have the same color. For example, the following graph can be 3-colored using the following color assignments: a=1,b=2,c=1,d%32,e=3,f=2.g33 a---b---c---g d Formulate the graph k-coloring problem as an evolutionary optimization. You may use a vector of integer representation, OR any representation that you think is more appropriate. you should specify: • A representation. • itness function. Give 3 examples of individuals and their fitness values if you are solving the above example. A set of mutation and/or crossover and/or repair operators. Intelligent operators that are suitable for this particular domain will earn…
A. Consider the following graphs: U Graph A Graph B 1.) Which of the following vertex sequence describe paths in the graph given above? a.) STUVWXZY b.) TVWZY c.) STUS d.) UYVTXZYU e.) WVUSTVW 2.) Which paths in no.1 are closed paths? Cycles? 3.) From the graph above determine the vertex sequence of the shortest path connecting the following pairs of vertex and give each length: a.)S & z b.)S & V c.) U & Y D.) U & X e.) V & W 4.) For each pair of vertex in no. 3 give the vertex sequence of the longest path connecting them that repeat no edges. Is there a longest path connecting them? 5.) How many spanning trees are can be generated from its graph? Define 2 spanning trees of Graph A and B. 6.) Which graph has and Euler path? Euler Circuit?(Use Fleury's Algorithm) For those that don't give an explanation? 7.) Which graph contains Hamiltonian Path? Hamiltonian Circuit? For those that don't give an explanation?
max edge distance Simplification key Figure 4-1: A sample process for the Douglas-Peucker algorithm The Douglas-Peucker algorithm is for the selection of representative points to simplify a curve composed of line segments. It uses a point-to-edge distance tolerance. The algorithm starts with a crude simplification that is the single edge joining the first and last vertices of the original polyline. It then computes the perpendicular distance of all intermediate vertices to that edge. The vertex that is furthest away from that edge, and that has a computed distance that is larger than a specified tolerance, will be marked as a key and added to the simplification. This process will recurse for each edge in the current simplification until all vertices of the original polyline are within tolerance of the simplification results. This process is illustrated in Figure 4-1. (1) Given three points (xp, Yp), (Xa, Ya), (Xp,Yb), show a detailed process to compute the perpendicular distance from p…
1) Find the adjacency matrix M for the following graph (see attached) 1a) Find M^2,M^3,M^4. What do the entries represent? Note that M^2,M^3,M^4 are matrix powers, not graph powers 1b) Express the transitive closure of a general graph G in terms of its adjacency matrix. That is, compute the adjacency matrix of G's transitive closure from G's adjacency matrix.
A directed graph G is defined using the following sets of vertices and edges. {n1, n2, n3, n4, N5, n6, n7, ng } E = {, , , , , , , , , } Q4) V = a) What is the adjacency matrix of G? b) List all semipaths of length 2 and 3. c) Give the condensation graph of G.
6. Refer to the following given graph: a) 2 1 3 ليا 3 3 5 2 8 Show the adjacency matrix for the graph. 7 2 5 6 b) List the nodes of the graph in ascending order using breadth-first traversal (the origin node is node 1). c) List all possible paths from vertex 5 to vertex 3. Then find the shortest path distance from vertex 5 to vertex 3.
2. Consider the graph given by the following adjacency list: vertex adjacent vertics 1 2, 3, 4 2 1 3 1, 4 4 1, 3 5 - (a) Draw the corresponding graph. (b) Write down the adjacency matrix A for this graph. Calculate A2. What is the meaning of the entries of matrices A and A2? (c) Starting at vertex 4, use the adjacency matrix algorithm to check for connectivity. Please no plagiarism and also i want clear hand writting. Thanks
a) Given the following directed graph: d b S с a e State the sequence of vertices visited using Breadth-First Search (BFS) Traversal, starting at vertex s.