Given a directed graph w/ nonnegative edge lengths & two distinct nodes, a and z. Let X denote a shortestpath 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-zpath.O i and iv onlyO iv onlyO None of the choicesO i onlyO i and iv onlyO iii onlyO ii only

solution: option (i) and option (iv) is correct. 1. i) X definitely remains a shortest a to z path…

Answered: Given a directed graph w/ nonnegative…

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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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
Question 8. A connected graph G has 4 vertices and 4 edges of costs 1, 2, 3 and respectively 4. (a) Show that G is not a tree. (b) Show that G has a single minimum spanning tree. (Hint: For example, think how Prim's algorithm constructs the minimum spanning tree). (c) Draw a connected graph G with 4 nodes and 4 edges of costs 1, 2, 3, 4, respectively, so that the minimum spanning tree contains the edge of cost 4. The 4 nodes are below, you need to draw the 4 edges and indicate their cost. a O b d
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
Algorithm : (1. Single-destination Shortest Path, 2. Bellman-Ford, 3. Negative-Weight Cycles), Dynamic Programming Define and prove a recurrence for the following problem: Given a directed graph G = (V, E) with edge weight function w : E → R and a source vertex s ∈ V , find a shortest path from s to v for every vertex v ∈ V .
please explain fully
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.
please answer both of the questions. 7. The Bellman-Ford algorithm for single-source shortest paths on a graph G(V,E) as discussed in class has a running time of O|V |3, where |V | is the number of vertices in the given graph. However, when the graph is sparse (i.e., |E| << |V |2), then this running time can be improved to O(|V ||E|). Describe how how this can be done.. 8. Let G(V,E) be an undirected graph such that each vertex has an even degree. Design an O(|V |+ |E|) time algorithm to direct the edges of G such that, for each vertex, the outdegree is equal to the indegree. Please give proper explanation and typed answer only.
Consider a directed graph G=(V,E) with n vertices, m edges, a starting vertex s∈V, real-valued edge lengths, and no negative cycles. Suppose you know that every shortest path in G from s to another vertex has at most k edges. How quickly can you solve the single-source shortest path problem? (Choose the strongest statement that is guaranteed to be true.) a) O(m+n) b) O(kn) c) O( km) d) O(mn)
We know that if the heuristic function in A* is good enough, then A* can always find a shortest weighted path between two vertices, and is generally much faster than Dijkstra. Assume we are using a graph where a good heuristic function is well defined for A*, such that A* can always find the same shortest paths as Dijkstra. Briefly explain when you should choose Dijkstra over A* in this case.
Please help with algorithm no coding needed
With a given graph below, run the Bellman-Ford Algorithm to find the shortest path from node s to all nodes. For example, (0, 100, 23, 300, 50) for (node 1, node 2, node 3, node 4, node 5)
My id last two digit : 21

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