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Next we turn to a miniaturized version of the kind of problem a network service provider might face Suppose we are managing a network whose lines have the bandwidths shown in Figure 73, and we need to establish three connections: between users A and B, between B and C, and between A and C Each connection requires at least two units of bandwidth, but can be assigned more Connection A B pays $3 per unit of bandwidth, and connections B C and A C pay $2 and $4, respectively Each connection can be routed in two ways, a long path and a short path, or by a combination: for instance, two units of bandwidth via the short route, one via the long route How do we route these connections to maximize our network s revenue This is a linear program We have variables for each connection and each path (long or short); for example, xAB is the short-path bandwidth allocated to the connection between A and B, and xAB the long-path bandwidth for this same connection We demand that no edge s 191

Part II:

tell the application id "commicrosoftentourage" set myTask to make new task with properties {name:"Clear out the filing cabinet", has due date:true, due date:date ("20 July 2010")} set priority of myTask to high set category of myTask to category "work" end tell

bandwidth is exceeded and that each connection gets a bandwidth of at least 2 units max 3xAB + 3xAB + 2xBC + 2xBC + 4xAC + 4xAC xAB + xAB + xBC + xBC 10 xBC + xBC + xAC + xAC 8 xAB + xBC + xAC 6 xAB + xAB + xAC + xAC 12 [edge (b, B)] [edge (a, A)] [edge (c, C)] [edge (a, b)] [edge (b, c)] [edge (a, c)]

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END; / PL/SQL procedure successfully completed dbvowner@aos> -- enable the OLS policy within DBV and dbvowner@aos> -- define the merge algorithm BEGIN dbms_macadmcreate_mac_policy( policy_name => 'CUSTOMER_POLICY' , algorithm => 'LII' ); END; / PL/SQL procedure successfully completed

To delete a task, identify it by its name property or, if you know the id property or the GUID property, use one of those for greater certainty For example, the following statement deletes the task named Clear out the filing cabinet, identifying it by the name property:

xAB + xBC + xAC 11 xBC + xBC 2 xAB , xAB , xBC , xBC , xAC , xAC 0 xAC + xAC 2 xAB + xAB 2

The algorithm LII means Least upper-bound of all levels, Intersection of compartments, Intersection of groups This algorithm is the most appropriate and most commonly used algorithm in commercial and government systems This algorithm and others are available with OLS and are described in the Label Security Administrator s Guide should you need to research them for your application s needs In our example, this algorithm basically means that the merging of the label LOW with a label of HIGH will result in LOW, or the least upper-bound of the levels We now need to configure DBV with the name(s) of the DBV factor(s) whose identities will be merged with the default OLS session label for a user using this algorithm Here we are simply using one factor, Connection_Type, and will use the PL/SQL procedure DBMS_MACADM ADD_POLICY_FACTOR to accomplish this

delete the task "Clear out the filing cabinet"

Even a tiny example like this one is hard to solve on one s own (try it!), and yet the optimal solution is obtained instantaneously via simplex: xAB = 0, xAB = 7, xBC = xBC = 15, xAC = 05, xAC = 45 This solution is not integral, but in the present application we don t need it to be, and thus no rounding is required Looking back at the original network, we see that every edge except a c is used at full capacity One cautionary observation: our LP has one variable for every possible path between the users In a larger network, there could easily be exponentially many such paths, and therefore this particular way of translating the network problem into an LP will not scale well We will see a cleverer and more scalable formulation in Section 72 Here s a parting question for you to consider Suppose we removed the constraint that each connection should receive at least two units of bandwidth Would the optimum change

dbvowner@aos> BEGIN dbms_macadmadd_policy_factor( policy_name => 'CUSTOMER_POLICY' , factor_name => 'Connection_Type' ); END; / PL/SQL procedure successfully completed

Entourage s notes are handy for keeping your information straight, particularly when you re working in Entourage and need to jot something down As you d expect, Entourage uses a note object to represent a note Table 16-14 explains the properties of the note object Most of these will probably seem familiar by now note Object Property

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