Let G=(V, E) represent a p-node, degree-d network. Any oblivious routing algorithm for routing p packets in G needs (√p/d) time in the worst case.
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- Given a mesh of p x p processors. Note that Exactly-One Partial Permutation Routing (EOPPR) is a special case of general routing problem. In EOPPR, each processor is the origin (and destination) of exactly one packet. This problem can be solved in <= 2(p-1) steps using Algorithm PPR given in the class. Note that there are always totally p x p packets. Give a best case and a worst case of using Algorithm PPR for a mesh of 5 x 5 processors. That is, (a) give a case that the run time is 1 for a mesh of 5 x 5 processors, and (b) give a case that that the run time is 2(5-1) = 8 for a mesh of 5 x 5 processors.Provided graph G=(N,E), in which N denotes the collection of routers and E, the collection of links. Calculate the least costly route from node U to all other nodes using Dijkstra's link-state routing mechanism, and then display the final lowest graph from U?QUESTION 4 Given G-({a, b, c d, e t.g h, LJ), E ) and JE| -45, how many different length-8 paths from a to b are there in G if G is undirected? Answer:
- Consider the ooding algorithm in an arbitrary network G = (V;E): 1) Eachnode acts as both a transmitter and a receiver, and 2) Each node tries toforward every message to every one of its neighbors except the source node.1. Formulate the algorithm in pseudo-code starting from a givennode.2. Prove that your algorithm is correct in that it terminates within nite time, and all entities will receive the information held by theinitiator.c) Given graph G = (N,E), where N is the set of routers and E is the set of links. Using Dijkstra's link-state routing algorithm ommute the least cost path from node U to all other nodes and show the resulting least-cost-path tree from U U 2 2 3 Y 2 2 3Create an algorithm for the Dijkstra Shortest Weighted Path based on the provided data.G is a weighted (directed or undirected) network, and s is a node in it.post-cond: specifies the shortest weighted route from s to each node of G, and d the lengths of those paths.
- 2. Find the costs of the cheapest paths from all nodes to F using Bellman-Ford algorithm. Show your work. В 3 4 3 A 1 F D EOur goal in this problem is to determine the “lowest latency routes” starting from your location. The internet in this problem is modeled by a graph, with vertices corresponding to other clients or servers, and edges representing the links between clients/servers. Each edge is not undirected, i.e., the links are unidirectional. At the same time, each link adds a constant latency if you use the link in your routes. Note that if you need to communicate with your own client, then the latency is 0. We represent your location as the vertex 0. Your goal is to determine the total latency it would take if you used the shortest path route from your location to any other client/server in the network. Input Format Each test case starts with a line containing three integers V, E, and Q, denoting the number of vertices, edges, and queries, respectively. Note that vertices are identified with integers from 0 to V-1. E lines follow, each containing three integers s_i, d_i, l_i, denoting the…Use the provided data to create the Dijkstra Shortest Weighted Path method.Precondition: S is a node in the weighted (directed or undirected) network G.Post-cond: specifies the shortest weighted route between each node of G and s, and d specifies the lengths of those paths.
- Consider an unstructured overlay network in which each node randomly chooses c neighbors. If P and Q are both neighbors of R, what is the probability that they are also neighbors of each other?For nodes 0000 and 1111, there exists four node-disjoint paths of length 4 (which happens to be the hamming distance between them). These paths are listed as travel from source 0000 through dimension 0-1-2-3 or 1-2-3-0 or 2-3-0-1 or 3-0-1-2 to the destination 1111. Question 1: how many node-disjoint paths between nodes 0000 and 1010 and what are their length? Question 2: for any two arbitrary nodes with the hamming distance r, how many node-disjoint paths among them with the distance r and what are they?Shown below is a network with cycles in it. The bridges run the distributed spanning tree algorithm. For all of the labeled ports, indicate the final state, assuming that B1 is the root bridge. Recall that RP = "Root Port," DP = "Designated Port," and BP = "Blocked Port." Carefully note the port numbers for each bridge when entering your answers! 1 B3 B8 2 2 E В K B1 T B4 B6 2 2 C 1 B5 1 3, B7 B2 2 W Bridge Port 1 Port 2 Port 3 B2 [ Select ] [ Select ] B3 [ Select ] [ Select ]