Exercise 3Consider calculation of PageRank for a directed graph. Consider two jumping probabilities a and B suchthat a > B. For every node u, let Pa(u) be the PageRank of u calculated using a and let Pg (u) be thePageRank of u calculated using B. For each of the following statements, indicate whether the statementis true or false and provide a brief explanation for your answer.1. The inequality Pa (u) > Pg (u) must hold for all nodes u.2. The inequality Pa(u) > Pg (u) must hold for at least one node u.

Answered: Exercise 3 Consider calculation of…

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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For each graph below, state the largest integer weight for directed edge (B,C) that makes the given description true. (Note that the edge weight need not be positive!)
a.Create any four scenarios that could possibly lead to deadlock.b. Use a directed graph to illustrate each of them.
Pick the correct statements for the attached directed graph for a toy world wide web. 1. There are exactly six columns having a 1 as an entry. 2. If a new edge from node I to F is added, the resulting graph is strongly connected. 3. The smallest non-zero element in the link matrix is 1/4. 4. The link matrix Q has a column of all zeros. 5. The link matrix is a reducible matrix.
True/False. Give a short explanation. i. Let T be a tree constructed by Dijkstra's algorithm for a weighted connected graph G. T is a spanning tree of G? ii. Let T be a tree constructed by Dijkstra's algorithm for a weighted connected graph G. T is a minimum spanning tree of G? iii. If an NP-complete problem can be solved in linear time, then all NP-complete problems can be solved in linear time. iv. If P # NP, there could be a polynomial-time algorithm for SAT.
Problem 2. Use Bellman-Ford to determine the shortest paths from vertex s to all other vertices in this graph. Afterwards, indicate to which vertices s has a well defined shortest path, and which do not by indicating the distance as -o∞. Draw the resulting shortest path tree containing the vertices with well defined shortest paths. For consistency, you should relax the edges in the following order: s → a, s → b, a → c, b → a, b → d, c → b, с — а, с —е, d — f, e — d and f — e. — а, b, а — с, b — а, b — d, с — b, → d and f -→e. a -1 3 5 -2 -5 S 4 4 10 6 b d f -10 -6
Consider the following two-person game on a general (not necessarily bipartite) graph G = (V, E). Players A and B alternate and each selects a (yet unchosen) edge e of the graph so that e together with the previously selected edges form a simple path. The first player unable to select such an edge loses. Show that if G has a perfect matching then player A has a winning strategy.
Consider a connected graph G with at least 4 edges that has all distinct edge weights. Which of the following properties must be true of a Minimum Spanning Tree (MST) of G? I. The MST must contain the shortest edge of G. II. The MST must contain the second-shortest edge of G. III. The MST can never contain the longest edge of G. None I Only I and II Only I and III Only O1, II, and III
Consider a weighted graph in which all the weights on the edges are distinct. Suppose that e is the edge with the largest weight. What is the property that the graph must have in order for e to be in the minimum spanning tree? Question options: 1) The graph must be a tree. 2) The edge e must be incident to a vertex of degree 1. 3) The weight of e must be close to the next largest weight. 4) The graph is no longer connected if e is removed.
in a graph G = (N,E,C), where N are nodes, E edges between nodes, and the weight of an edge e ∈ E is given by C(e), where C(e) > 1, for all e ∈ E. the heuristic h that counts the least amount of edges from an initial state to a goal state. now removing edges from the graph, while keeping the heuristic values unchanged. Is the heuristic still consistent?
Given a directed graph w/ nonnegative edge lengths & two distinct nodes, a and z. Let X denote a shortest path from a to z. If we add 10 to the length of every edge in the graph, then: i) X definitely remains a shortest a-z path. ii) X definitely does not remain a shortest a-z path. iii) X might or might not remain a shortest a-z path (depending on the graph). iv) If X has only one edge, then X definitely remains a shortest a-z path. O i and iv only O iv only O None of the choices O i only O i and iv only O iii only O ii only
Consider a graph with five nodes labeled A, B, C, D, and E. Let's say we have the following edges with their weights: A to B with weight 3 A to C with weight 1 B to C with weight 2 B to D with weight 1 C to E with weight 4 D to E with weight 2 a. Find the shortest path from A to E using Dijkstra's algorithm b. Use Prim to find the MST c. Use Kruskal to find the MST d. What's the difference between Prim and Kruskal algorithms? Do they always have the same result? Why or why not.
Consider a random graph G(N, p) with In the limit N → ∞ the average degree (k) is given by 2/3 None of the above Therefore the random graph has not has a giant component in the limit N → ∞. P = e² In 2 3N

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