Explain..........Multiple answers allowed Given a directed graph G with 2 strongly connect components C1 and C2, which of thefollowing statement(s) is true?O If v1 and v2 are members of C1, there must be a path from v1 ~ v2O If v1 and v2 are members of C2, there must be a path from v2 - v1O If v1 is a member of C1 and v2 is a member of C2, there must be a path from v2 ~ v1O If v1 is a member of C1 and v2 is a member of C2, there must be a path from v1 ~ v2

A directed graph is strongly connected if there is a path between all pairs of vertices. A strongly…

Given a directed graph G with 2 strongly connect components C1 and C2, which of the following statement(s) is true? If v1 and v2 are members of C1, there must be a path from v1 ~ v2 If v1 and v2 are members of C2, there must be a path from v2 ~ v1 If v1 is a member of C1 and v2 is a member of C2, there must be a path from v2 ~ v1 O If v1 is a member of C1 and v2 is a member of C2, there must be a path from v1 ~ v2

Given a directed graph G with 2 strongly connect components C1 and C2, which of the following statement(s) is true? If v1 and v2 are members of C1, there must be a path from v1 ~ v2 If v1 and v2 are members of C2, there must be a path from v2 ~ v1 If v1 is a member of C1 and v2 is a member of C2, there must be a path from v2 ~ v1 O If v1 is a member of C1 and v2 is a member of C2, there must be a path from v1 ~ v2

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

See similar textbooks

Similar questions

Consider a graph with nodes and directed edges and let an edge from node a to node b berepresented by a fact edge (a,b). Define a binary predicate path that is true for nodes c and dif, and only if, there is a path from c to d in the graph.
Every pair of vertices in a graph that is linked by two different paths is said to be biconnected. An articulation point in a connected graph is a vertex that, if it and its surrounding edges were eliminated, would cause the graph to become disconnected. demonstrate the biconnection of any graph lacking articulation points. Tip: To create two disjoint paths connecting s and t given a set of vertices s and t and a path connecting them, take advantage of the fact that none of the vertices on the path are articulation points.
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…
A directed graph G= (V,E) consists of a set of vertices V, and a set of edges E such that each element e in E is an ordered pair (u,v), denoting an edge directed from u to v. In a directed graph, a directed cycle of length three is a triple of vertices (x,y,z) such that each of (x,y) (y,z) and (z,x) is an edge in E. Write a Mapreduce algorithm whose input is a directed graph presented as a list of edges (on a file in HDFS), and whose output is the list of all directed cycles of length three in G. Write the pseudocode for the mappers/reducers methods. Also, assuming that there are M mappers, R reducers, m edges and n vertices -- analyze the (upper-bound of the) communication cost(s).
Let G be a directed graph where each edge is colored either red, white, or blue. A walk in G is called a patriotic walk if its sequence of edge colors is red, white, blue, red, white, blue, and soon. Formally ,a walk v0 →v1 →...vk is a patriotic walk if for all 0≤i<k, the edge vi →vi+1 is red if i mod3=0, white if i mod3=1,and blue if i mod3=2. Given a graph G, you wish to find all vertices in G that can be reached from a given vertex v by a patriotic walk. Show that this can be accomplished by efficiently constructing a new graph G′ from G, such that the answer is determined by a single call to DFS in G′. Do not forget to analyze your algorithm.
(a) Show that a graph G with at least three vertices is 2-connected if and only if any vertex and any edge of G lie on a common cycle of G: (b) Show that a graph G with at least three vertices is 2-connected if and only if any two edges of G lie on a common cycle
Question 1: In graph theory, a graph X is a "complement" of a graph F if which of the following is true? Select one: a. If X is isomorph to F, then X is a complement of F. b. If X has half of the vertices of F (or if F has half of the vertices of X) then X is a complement of F. c. If X has the same vertex set as F, and as its edges ONLY all possible edges NOT contained in F, then X is a complement of F. d. If X is NOT isomorph to F, then X is a complement of F. Question 2: Which statement is NOT true about Merge Sort Algorithm: Select one: a. Merge Sort time complexity for worst case scenarios is: O(n log n) b. Merge Sort is a quadratic sorting algorithm c. Merge Sort key disadvantage is space overhead as compared to Bubble Sort, Selection Sort and Insertion Sort. d. Merge Sort adopts recursive approach
For each pair of graphs G1 = <V1, E1> and G2 = <V2, E2> a) determine if they are isomorphic or not. b) Determine a function that can be isomorphic between them if they are isomorphic. Otherwise you should justify why they are not isomorphic. c) is there an Euler road or an Euler bike in anyone graph? Is Hamilton available? You should draw if the answer is yes and reason if your answer is no.
Consider a directed graph G with a starting vertex s, a destination t, and nonnegative edge lengths. Under what conditions is the shortest s-t path guaranteed to be unique? a) When all edge lengths are distinct positive integers. b) When all edge lengths are distinct powers of 2. c) When all edge lengths are distinct positive integers and the graph G contains no directed cycles. d) None of the other options are correct.
(1) Given a weighted directed graph G = (V, E, w), where V = {1, 2, 3, 4}, E ={(1,3), (2,1), (2,4), (3,2), (4,1), (4,3)}, and w(1,3) = −2, w(2,1) = 1, w(2,4) = 2,w(3,2) = 4, w(4,1) = −3, w(4,3) = 3. (a) Represent the graph G graphically;(b) Run SLOW-ALL-PAIRS-SHORTEST-PATHS on the above graph and show the matricesL(k) that result for each iteration of the loop. (2) Discuss how to use the Floyd-Warshall algorithm to detect a negative-weight cycle. (3) The essence of Johnson’s algorithm is re-weighting so that a transformed graph has no negativeweight edges, which enables the use of Dijkstra’s algorithm. Let us modify Johnson’s algorithmsuch that G' = G and s be any vertex. (a) Give a counter example (i.e. a simple weighted and directed graph) to show thismodification is incorrect assuming ∞ − ∞ is undefined(b) Show (using logical arguments) this modification produces the correct results when a givenG is strongly connected.
Every set of vertices in a graph is biconnected if they are connected by two disjoint paths. In a connected graph, an articulation point is a vertex that would disconnect the graph if it (and its neighbouring edges) were removed. Demonstrate that any graph that lacks articulation points is biconnected. Given two vertices s and t and a path connecting them, use the knowledge that none of the vertices on the path are articulation points to create two disjoint paths connecting s and t.
Every pair of vertices in a network that is connected by two different pathways is said to be biconnected. An articulation point in a connected network is a vertex that, if it and its surrounding edges were removed, would cause the graph to become disconnected. demonstrate the biconnection of any graph lacking articulation points. Tip: To create two disjoint pathways linking s and t given a set of vertices s and t and a path connecting them, take use of the fact that none of the vertices on the path are articulation points.