Distributed Database Management Systems: Lecture 18

Distributed Database Management Systems: Lecture 18. The main topics covered in this chapter include: continue with VF to global affinity measure; bond energy algorithm; find the combination that has the maximum Affinity Measure;...

Distributed Database Management Systems Lecture 18 In the previous lecture • Continue with VF – Information Requirement – Attribute affinities Virtual University of Pakistan In this Lecture • Continue with VF – Global Affinity Measure – Bond Energy Algorithm Virtual University of Pakistan n n ∑ ∑ aff(Ai, Aj) [aff(Ai, Aj­1) + aff(Ai, Aj+1)                + aff(A ) + aff(A i­1, A i+1, Aj) ] A A A j A AM =  i = 1 j = 1 A1 45 45 A2 80 75 A3 45 53 A4 75 78 Virtual University of Pakistan The AA is symmetric so  A1 A2 A3 A4 A1 45 45 A2 80 75 A3 45 53 A4 75 78 Virtual University of Pakistan Rather than taking n n ∑ ∑ aff(Ai, Aj) [aff(Ai, Aj­1) + aff(Ai, Aj+1)                + aff(Ai­1, Aj) + aff(Ai+1, Aj) ] AM =  i = 1 j = 1 We take only n n n ∑ aff(A , A ) aff(A , A ∑ ∑ aff(Ai, Aj) aff(Ai, Aj­1) + AM =  i = 1 j = 1 i = 1 n Let bond(Ax, Ay) =  ∑ i j aff(Az, Ax)aff(Az, Ay) z = 1 n ∑ bond(Aj, Aj­1) +bond(Aj, Aj+1) AM =  j = 1 Virtual University of Pakistan i ) j+1 n ∑ AM =  j = 1 bond(Aj, Aj­1) +bond(Aj, Aj+1) J=1 45 45 0 80 75 45 53 75 78 Virtual University of Pakistan n ∑ AM =  j = 1 bond(Aj, Aj­1) +bond(Aj, Aj+1) J=2 45 45 0 80 75 45 53 75 78 Virtual University of Pakistan n ∑ AM =  j = 1 bond(Aj, Aj­1) +bond(Aj, Aj+1) J=4 45 45 0 80 75 45 53 75 78 Virtual University of Pakistan Approach for VF • Find the combination that has the maximum Affinity Measure • It will represent best grouping among attributes Virtual University of Pakistan 10 • We can find all possible AMs or • We can use the BEA (Bond Energy Algorithm) Virtual University of Pakistan 11 Bond Energy Algorithm A1, A2, …, Ai-1, Ai, Aj, Aj+1, ……, An AM1 AM2 AM3 AMold = AM1 + AM2+ AM3 AM2 involves Bond(Ai, Aj) twice Virtual University of Pakistan 12 BEA A1, A2, …, Ai-1, Ai, Ak, Aj, Aj+1, ……, An AM1 AM2 AM3 AMnew = AM1 + AM2+ AM3 AM2 involves Bond(Ai, Ak) and Bond(Ak, Aj) twice Virtual University of Pakistan 13 BEA Contribution cont(Ai, Ak, Aj) is the contribution in AM when placing Ak between Ai and Aj Cont(Ai, Ak, Aj) = AMnew- AMold = 2Bond(Ai,Ak) + 2Bond(Aj, Ak) – 2Bond(Ai, Aj) Virtual University of Pakistan 14 Steps in BEA Virtual University of Pakistan 15 • Input: The AA matrix • Output: The clustered affinity matrix CA which is a permutation of AA • Initialization: Place and fix one of the columns of AA in CA • Iteration: Place the remaining n-i columns in the remaining i+1 positions in the CA matrix For each column, choose the placement that makes the most contribution to the global affinity measure • Row order: Order the rows according to the column ordering Virtual University of Pakistan 16 Bond Energy Algorithm Virtual University of Pakistan 17 • • • Input AA Output CA Begin CA (•, 1) ← AA (•, 1) CA (•, 2) ← AA (•, 2) Index ← Virtual University of Pakistan 18 While index ≤ n Begin For I from to index –1 by calculate cont(Ai-1, Aindex, Ai) end-for Calculate cont(Aindex-1, Aindex, Aindex+1) Loc ← placement given by maximum cont value For j from index to loc by –1 CA (•, j) ← AA (•, j-1) end-for CA (•, loc) ← AA (•, index) Index ← index + End-while Order the rows according to relative order of columns End {BEA} Virtual University of Pakistan 19 Thanks Virtual University of Pakistan 20 ...In the previous lecture • Continue with VF – Information Requirement – Attribute affinities Virtual University of Pakistan In this Lecture • Continue with VF – Global Affinity... Output CA Begin CA (•, 1) ← AA (•, 1) CA (•, 2) ← AA (•, 2) Index ← Virtual University of Pakistan 18 While index ≤ n Begin For I from to index –1 by calculate cont(Ai-1, Aindex, Ai) end-for Calculate