Distributed Database Management Systems: Lecture 14. The main topics covered in this chapter include: minterm predicates; PHF-requirements; minterm selectivities sel(mi); access frequencies acc(qi); access frequencies minterm acc(mi); completeness example;...
Distributed Database Management Systems Lecture 14 Minterm predicates: given a set of simple predicates Pr = {pr1, pr2, …, pm}for a relation R, the set of minterm predicates M is defined as Virtual University of Pakistan M = {m1, m2, ……, mz} M = {mj | mj = p*k}, ≤ k ≤ m, ≤ j ≤z p ∈ Pr k where p*k = pk or p*k = (pk) Virtual University of Pakistan PAY(title, sal) p1: title = “El Eng” p2: title = “Sys Ana” p3: title = “Mech Eng” p4: title = “Prog” p5: SAL ≤ 20,000 p6: SAL > 20000 Virtual University of Pakistan Minterm Predicates Virtual University of Pakistan m1: title = “El Eng” m2: title = “Sys Ana” Virtual University of Pakistan SAL ≤ 20,000 SAL > 20,000 PHF-Requirements 3- minterm selectivities sel(mi): number of tuples of the relation that would be accessed by a user query involving mi Like, sel(m1) = as per data on p108 Virtual University of Pakistan 4- Access frequencies acc(qi): frequency with which user applications access data If Q(q1, q2, …, qn} is set of user queries, then acc(qi) determines the access frequency of qi within a given period, like acc(q2) = 24 5- Access frequencies minterm acc(mi) can also be defined from acc(q ) i Virtual University of Pakistan • A PHF is defined by a selection operation on the owner relations of the database schema, given a relation R, its PHF are given by Ri = Fi (R), ≤ i ≤ w – Where Fj is a selection formula, which is (preferably) a minterm predicate Virtual University of Pakistan PHF (Simple Example) Virtual University of Pakistan 10 PAY Title Sal Elect Eng 40000 Sys Analyst 34000 Mech Eng 27000 Programmer 24000 Virtual University of Pakistan 11 PAY1 = σ sal ≤ 30000 (PAY) PAY2 = σ sal > 30000 (PAY) Virtual University of Pakistan 12 Title Sal Elect Eng 40000 Sys Analyst 34000 PAY1 PAY2 Title Sal Mech Eng 27000 Programmer 24000 Virtual University of Pakistan 13 • Defining simple predicates may be tricky – in case of continuous domain – Balance in Fragments’ Size Virtual University of Pakistan 14 A set of simple predicates Pr is said to be complete if the accesses to the tuples of the minterm fragments defined on Pr requires that two tuples of the same minterm fragment have the same probability of being accessed by the application Virtual University of Pakistan 15 Completeness Example Virtual University of Pakistan 16 PROJ pNo pName budget Loc P1 Instrumentation 3.5M Lahore P2 Database Dev 2.3M Rawalpindi P3 CAD/CAM 1.9M Rawalpindi P4 Maintenance 1.6M Peshawar Virtual University of Pakistan 17 –Find the budgets of projects at each location (1) –Find projects with budgets less than 2M (2) Virtual University of Pakistan 18 • According to (1), Pr = {LOC=“Lahore”, LOC=“Rawalpindi”, LOC=“Peshawar”} • Which is not complete with respect to (2) Virtual University of Pakistan 19 Modify Pr = {LOC=“Lahore”, LOC=“Rawalpindi”, LOC=“Peshawar”, BUDGET200000} • Which is complete Virtual University of Pakistan 20 Thanks ... University of Pakistan • A PHF is defined by a selection operation on the owner relations of the database schema, given a relation R, its PHF are given by Ri = Fi (R), ≤ i ≤ w – Where Fj is a selection... tricky – in case of continuous domain – Balance in Fragments’ Size Virtual University of Pakistan 14 A set of simple predicates Pr is said to be complete if the accesses to the tuples of the minterm... Example Virtual University of Pakistan 16 PROJ pNo pName budget Loc P1 Instrumentation 3.5M Lahore P2 Database Dev 2.3M Rawalpindi P3 CAD/CAM 1.9M Rawalpindi P4 Maintenance 1.6M Peshawar Virtual University