Computer networks typically consist of nodes and edges-they

Question

Computer Networks, Distributed Systems, and Mobile Agents

Computer networks typically consist of nodes and edges-they are graphs. The nodes can typically be computers, routers, servers, and so on. The edges indicate a communication path between nodes. Assume you are a network administrator for a distributed system and that you wish to perform maintenance of all the servers in your system. You have decided to do this by using a mobile agent. To get started, look up and answer the questions in Part 1. After that, complete Part 2:

Part 1

1. What is a distributed system?
2. What is a mobile agent?

Since this agent is autonomous and moves from computer to computer, it would be smart to equip it with shortest path algorithms, so that it can go from server to server, reaching all the servers only once, in the shortest amount of time. This is the traveling sales person (TSP) problem. Note that computer networks can be modeled using graphs and that shortest paths solutions, Hamilton cycles, TSP, and so on can be found using graph-based algorithms.

Part 2

1. How would you model a computer network using a graph? What are potential nodes, edges, and weights?
2. Which of these traversal algorithms should the agent be equipped with? Which will help the agent traverse the network in an efficient manner? Explain why.
3. What is the TSP problem, and how does it relate to this question?

Review the Discussion Participation Scoring Guide prior to posting.

Part three

Graph Applications and the Traveling Salesperson

In the class discussions, we have talked about how the traveling salesperson (TSP) problem and how it can be modeled using graphs. We also looked at finding a minimum length in a graph as well as Hamiltonian cycles.

Graphs, graph algorithms and methods, and graph theory are integral to IT and computer science applications and coding. For this assignment, write a two- to three-page paper that responds to each of the following questions:

1. What is a Hamiltonian cycle?
2. What is a Euler cycle?
3. What is a minimum length Hamiltonian cycle?
4. Given a graph with n edges, what is the time complexity of finding a Euler path? Is this a polynomial time algorithm? Explain and show all work and the graph. Hint: Include the algorithm and pseudocode.
5. Given a graph with n edges, can one find a minimum Hamiltonian cycle (TSP) in polynomial time? Has anyone ever proved that a polynomial time algorithm does not exist for this problem? Explain your answers and show the graph. Hint: Consider NP complete problems.
6. Offer one example of an IT or computer application that can be modeled as the TSP problem. This must be at least one paragraph.

Your calculations and work must be shown. Include references to any resources you use to complete the assignment.