How to Build Network?How to Build Network?

ISAT 625ISAT 625

Network ProblemsNetwork Problems

Build highways to connect citiesBuild highways to connect cities Build network to connect computers Build network to connect computers Layout water pipelines for a cityLayout water pipelines for a city Find the best route to driveFind the best route to drive Products, mail deliveryProducts, mail delivery

Spanning Tree ProblemSpanning Tree Problem

Telecommunications NetworkTelecommunications Network Connect computer systems and devices together in an Connect computer systems and devices together in an

efficient and effective mannerefficient and effective manner

DEC was concerned how computer systems and devices DEC was concerned how computer systems and devices were connected to a LAN using Ethernet.were connected to a LAN using Ethernet.

““I think I shall never see a graph more lovely than a tree. A tree 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 whose critical property is loop-free connectivity. A tree must be sure to span, so packet can reach every LAN. First the route 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 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 are traced. In the tree these paths are placed. A mesh is made for folks by me, then bridges find a spanning tree.for folks by me, then bridges find a spanning tree.

Minimal-Spanning Tree Minimal-Spanning Tree TechniqueTechnique

ObjectiveObjectiveConnect all nodes of a network together while Connect all nodes of a network together while

minimizing the total distanceminimizing the total distance

ExampleExampleConsider the Lauderale Construction Company, Consider the Lauderale Construction Company,

which is currently developing a luxurious housing project which is currently developing a luxurious housing project on Panama City Beach. Melvin Lauderdale, owner and on Panama City Beach. Melvin Lauderdale, owner and president of the company, must determine the least president of the company, must determine the least expensive way to provide water and power to each house.expensive way to provide water and power to each house.

Minimal-Spanning TreeMinimal-Spanning Tree

Minimal-Spanning TreeMinimal-Spanning Tree

Steps for the Minimal-Spanning Tree TechniqueSteps for the Minimal-Spanning Tree Technique1.1. Select any node in the networkSelect any node in the network

2.2. Connect this node to the nearest node that minimizes Connect this node to the nearest node that minimizes the total distancethe total distance

3.3. Considering all of the nodes that are now connected, Considering all of the nodes that are now connected, find and connected the nearest node that is not find and connected the nearest node that is not connectedconnected

4.4. Repeat Step 3 until all nodes are connectedRepeat Step 3 until all nodes are connected

Maximal-Flow ModelsMaximal-Flow Models

GoalGoalFind the maximum amount of material, traffic, Find the maximum amount of material, traffic,

or information that can flow through a network from or information that can flow through a network from one point to another pointone point to another point

ExampleExampleWaukesha, a small town in Wisconsin, is in the Waukesha, a small town in Wisconsin, is in the

process of developing a road system for the downtown process of developing a road system for the downtown area. Bill Blackstone, one of the city planners, would area. Bill Blackstone, one of the city planners, would like to determine the maximum number of cars that like to determine the maximum number of cars that can flow through the town from west to east.can flow through the town from west to east.

Maximal-Flow ModelsMaximal-Flow Models

Maximal-Flow ModelsMaximal-Flow Models

Steps of Maximal-Flow TechniqueSteps of Maximal-Flow Technique1.1. Pick any path with some flowPick any path with some flow

2.2. Increase the flow as much as possibleIncrease the flow as much as possible

3.3. Adjust the flow capacity numbers on the pathAdjust the flow capacity numbers on the path

4.4. Repeat these steps until an increase in flow is Repeat these steps until an increase in flow is no longer possibleno longer possible

Shortest-Route ModelsShortest-Route Models

GoalGoalFind the shortest path that you can travel Find the shortest path that you can travel

from one point to a another point in the networkfrom one point to a another point in the network

ExampleExampleEvery day, Ray Design, INC., must Every day, Ray Design, INC., must

transport beds, chairs, and other furniture items transport beds, chairs, and other furniture items from the factory to the warehouse. This involves from the factory to the warehouse. This involves going through several cities. Ray would like to going through several cities. Ray would like to find the route with the shortest distance.find the route with the shortest distance.

Shortest-Route ModelsShortest-Route Models

Shortest-Route ModelsShortest-Route Models

Steps of the Shortest-Route TechniqueSteps of the Shortest-Route Technique1.1. Find the nearest node to the origin. Put the Find the nearest node to the origin. Put the

distance in a box by the nodedistance in a box by the node

2.2. Find the next-nearest node to the origin, and Find the next-nearest node to the origin, and put the distance in a box bu the node.put the distance in a box bu the node.

3.3. Repeat this process until you have gone Repeat this process until you have gone through the networkthrough the network

PetroChemPetroChem

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

PetroChemPetroChem

Location ProblemLocation Problem

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

ExampleExample

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