10_Vertical_Partitioning_Handout

10_Vertical_Partitioning_Handout - Vertical Partitioning...

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Vertical Partitioning – Chap. 5 of Ozsu I. Vertical partitioning is complex A. If number of non-key columns = m, the number of possible fragments is the m th Bell number B(m) m m for large m B. This is a big number Frag(a,b) = a, b | ab B(2) = 2 Frag(a,b,c) = a, Frag(b,c) | ab, c | ac, b | abc B(3) = 5 Frag(a,b,c,d) = a, Frag(b,c,d) | ab, Frag(c,d) | ac, Frag(b,d) | ad, Frag(b,c) | abc, d | abd, c | acd, b | abcd B(4) = 15 Frag(a,b,c,d,e) = a, Frag(b,c,d,e) | ab, Frag(c,d,e) | ac, Frag(b,d,e) | ad, Frag(b,c,e) | ae, Frag(b,c,d) | abc, Frag(c,d) | abd, Frag(c,e) | abe, Frag(c,d) | acd, Frag(b,e) | ace, Frag(b,d) | ade, Frag(b,c) | abcd, e | abce, d | abde, c | acde, b | abcd B(5) = 52 II. Sample clustering q 1 : SELECT budget FROM proj WHERE pno = value q 2 : SELECT pname, budget FROM proj q 3 : SELECT pname FROM proj WHERE loc = value q 4 : SELECT sum(budget) FROM proj WHERE loc = value A. Define a matrix from the use() function A 1 (pno) A 2 (pname) A 3 (budget) A 4 (loc) q 1 1 0 1 0 q 2 0 1 1 0 q 3 0 1 0 1 q 4 0 0 1 1 B. This does not help us because we don't know the access frequency of the attributes C. We need the access frequency to calculate attribute affinity between two columns A i , A j aff (A i , A j ) D. The attribute affinity between two attributes A i and A j of a relation (k|use(q k ,A i k ,A j )) ( 2200 PAY l ) [ ref l (q k ) acc l (q k ) ] where: ref l (q k ) is the number of access to attributes A i and A j for each application q k at site S l and acc l (q k ) is the access frequency of q k for each site

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E. Suppose 3 sites and ref
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10_Vertical_Partitioning_Handout - Vertical Partitioning...

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