How to Build Network?

1. How to Build Network? ISAT 625

2. Network Problems • Build highways to connect cities • Build network to connect computers • Layout water pipelines for a city • Find the best route to drive • Products, mail delivery

4. Spanning Tree Problem • Telecommunications Network • Connect computer systems and devices together in an efficient and effective manner DEC was concerned how computer systems and devices were connected to a LAN using Ethernet. “I think I shall never see a graph more lovely than a tree. A tree whose critical property is loop-free connectivity. A tree must be sure to span, so packet can reach every LAN. First the route must be selected, by ID it is elected. Least-cost from the root are traced. In the tree these paths are placed. A mesh is made for folks by me, then bridges find a spanning tree.

5. Minimal-Spanning Tree Technique Objective Connect all nodes of a network together while minimizing the total distance Example Consider the Lauderale Construction Company, which is currently developing a luxurious housing project on Panama City Beach. Melvin Lauderdale, owner and president of the company, must determine the least expensive way to provide water and power to each house.

6. Minimal-Spanning Tree

7. Minimal-Spanning Tree Steps for the Minimal-Spanning Tree Technique • Select any node in the network • Connect this node to the nearest node that minimizes the total distance • Considering all of the nodes that are now connected, find and connected the nearest node that is not connected • Repeat Step 3 until all nodes are connected

8. Maximal-Flow Models Goal Find the maximum amount of material, traffic, or information that can flow through a network from one point to another point Example Waukesha, a small town in Wisconsin, is in the process of developing a road system for the downtown area. Bill Blackstone, one of the city planners, would like to determine the maximum number of cars that can flow through the town from west to east.

9. Maximal-Flow Models

10. Maximal-Flow Models Steps of Maximal-Flow Technique • Pick any path with some flow • Increase the flow as much as possible • Adjust the flow capacity numbers on the path • Repeat these steps until an increase in flow is no longer possible

11. Shortest-Route Models Goal Find the shortest path that you can travel from one point to a another point in the network Example Every day, Ray Design, INC., must transport beds, chairs, and other furniture items from the factory to the warehouse. This involves going through several cities. Ray would like to find the route with the shortest distance.

12. Shortest-Route Models

13. Shortest-Route Models Steps of the Shortest-Route Technique • Find the nearest node to the origin. Put the distance in a box by the node • Find the next-nearest node to the origin, and put the distance in a box bu the node. • Repeat this process until you have gone through the network

14. PetroChem PetroChem, an oil refinery located on the Mississippi River south of Baton Rouge is designing a new plant to produce diesel fuel. The picture below shows the network of the main processing centers along with the existing rate of flow (in thousands of gallons of fuel). The management at PetroChem would like to determine the maximum amount of fuel that can flow through the plant.

15. PetroChem

16. Location Problem • A location problem is concerned with a situation which can be represented by a network, and in which we wish to locate some facility or facilities so that some function is maximized or minimized

17. Example Suppose that we wish to locate a hospital, police station, fire station or some other service point at one of the towns in a region. In this case, the vertices of the network correspond to the towns, and the edges correspond to roads linking these towns.