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Sometimes a computational task is suf ciently general that any subroutine for it can also be used to solve a variety of other tasks, which at rst glance might seem unrelated For instance, we saw in 6 how an algorithm for nding the longest path in a dag can, surprisingly, also be used for nding longest increasing subsequences We describe this phenomenon by saying that the longest increasing subsequence problem reduces to the longest path problem in a dag In turn, the longest path in a dag reduces to the shortest path in a dag; here s how a subroutine for the latter can be used to solve the former: function LONGEST PATH(G) negate all edge weights of G return SHORTEST PATH(G) Let s step back and take a slightly more formal view of reductions If any subroutine for task Q can also be used to solve P , we say P reduces to Q Often, P is solvable by a single call to Q s subroutine, which means any instance x of P can be transformed into an instance y of Q such that P (x) can be deduced from Q(y):

Note that the DBV integration with OLS does in fact support the merging of multiple factors with OLS The final step in our configuration is to associate an OLS label from the policy to each DBV identity for the DBV factor Connection_Type This can be accomplished using the PL/SQL procedure DBMS_MACADMCREATE_POLICY_LABEL:

dbvowner@aos> -- we will assign the LOCAL_DBA identity dbvowner@aos> -- an OLS label of HIGH dbvowner@aos> BEGIN dbms_macadmCREATE_POLICY_LABEL( identity_factor_name => 'Connection_Type' , identity_factor_value => 'LOCAL_DBA' , policy_name => 'CUSTOMER_POLICY' , label => 'HIGH' ); END; / PL/SQL procedure successfully completed

name ID GUID iCal data content modification date category project list project sharing list links creation date

P (x)

5:

Editor automatically indents the nested tell block so that it is easy to read:

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(Do you see that the reduction from P = LONGEST PATH to Q = SHORTEST PATH follows this schema ) If the pre- and postprocessing procedures are ef ciently computable then this creates an ef cient algorithm for P out of any ef cient algorithm for Q! Reductions enhance the power of algorithms: Once we have an algorithm for problem Q (which could be shortest path, for example) we can use it to solve other problems In fact, most of the computational tasks we study in this book are considered core computer science problems precisely because they arise in so many different applications, which is another way of saying that many problems reduce to them This is especially true of linear programming

dbvowner@aos> -- we will assign the CORPORATE_SSL identity dbvowner@aos> -- an OLS label of HIGH dbvowner@aos> BEGIN dbms_macadmCREATE_POLICY_LABEL( identity_factor_name => 'Connection_Type' , identity_factor_value => 'CORPORATE_SSL' , policy_name => 'CUSTOMER_POLICY' , label => 'HIGH' ); END; / PL/SQL procedure successfully completed dbvowner@aos> -- we will assign the CORPORATE_PASSWORD identity dbvowner@aos> -- an OLS label of HIGH dbvowner@aos> BEGIN dbms_macadmCREATE_POLICY_LABEL( identity_factor_name => 'Connection_Type' , identity_factor_value => 'CORPORATE_PASSWORD' , policy_name => 'CUSTOMER_POLICY' , label => 'HIGH' ); END; / PL/SQL procedure successfully completed dbvowner@aos> -- we will assign the OTHER identity dbvowner@aos> -- an OLS label of LOW dbvowner@aos> BEGIN dbms_macadmCREATE_POLICY_LABEL( identity_factor_name => 'Connection_Type' , identity_factor_value => 'OTHER' , policy_name => 'CUSTOMER_POLICY' , label => 'LOW' ); END; / PL/SQL procedure successfully completed dbvowner@aos> COMMIT; Commit complete

(*Start a tell block to the Finder Open a window to the Documents folder Set the view to Column view *) tell the application "Finder"

As evidenced in our examples, a general linear program has many degrees of freedom 1 It can be either a maximization or a minimization problem 2 Its constraints can be equations and/or inequalities 3 The variables are often restricted to be nonnegative, but they can also be unrestricted in sign 193

We now want to examine how our policy behaves using the scenario in which MARY is querying the SHCUSTOMERS table from within the corporate network In this scenario, we expect MARY to be able to see all customers no matter what their credit limit In addition, we expect the effective OLS session label to be the maximum label MARY is authorized to see HIGH

open folder "Documents" of home tell the front Finder window set bounds to {1, 44, 800, 605} set current view to column view set target to folder "Applications" of startup disk end tell end tell

We will now show that these various LP options can all be reduced to one another via simple transformations Here s how 1 To turn a maximization problem into a minimization (or vice versa), just multiply the coef cients of the objective function by 1 2a To turn an inequality constraint like variable s and use

mary@aos> -- show the Connection_Type factor and session context mary@aos>SELECT DVSYSGET_FACTOR('Connection_Type') Connection_Type , DVSYSGET_FACTOR('Authentication_Method') Authentication_Method , DVSYSGET_FACTOR('Client_IP') Client_IP FROM DUAL;

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