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91 92 93 94 95 A₁ A2 A3 A4 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 (a) A5 0 1 0 1 1 1 0 0 0 0 S₁ S₂ S3 91 10 20 0 92 5 0 10 93 0 35 5 94 0 10 0 95 0 15 0 (b)

91 92 93 94 95 A₁ A2 A3 A4 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 (a) A5 0 1 0 1 1 1 0 0 0 0 S₁ S₂ S3 91 10 20 0 92 5 0 10 93 0 35 5 94 0 10 0 95 0 15 0 (b)

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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 Let Q ={q1,...,q5} be a set of queries, A ={A1,..., A5} be a set of attributes, and S ={S1,S2,S3} be a set of sites. The matrix of Fig. 2.25a describes the attribute usage values and the matrix of Fig. 2.25b gives the application access frequencies. Assume that refi(qk) =1forall qk and Si and that A1 is the key attribute. Use the bond energy and vertical partitioning algorithms to obtain a vertical fragmentation of the set of attributes in A

**Exercise: Attribute Affinity Matrix (AA) Fill-in** **Objective:** Complete the blanks to form the attribute affinity matrix (AA) based on Problem 2.6 in the textbook. Each blank must be filled with a numeric value without any spaces. **Matrix Structure:** | | A1 | A2 | A3 | A4 | A5 | |-----|----|----|----|----|----| | A1 | - | a | b | c | d | | A2 | e | - | f | g | h | | A3 | p | q | - | r | s | | A4 | t | u | v | - | w | | A5 | x | y | z | k | - | **Fill in the following:** - a = [type your answer...] - b = [type your answer...] - c = [type your answer...] - d = [type your answer...] - e = [type your answer...] - f = [type your answer...] - g = [type your answer...] - h = [type your answer...] - p = [type your answer...] - q = [type your answer...] - r = [type your answer...] - s = [type your answer...] - t = [type your answer...] - u = [type your answer...] - v = [type your answer...] - w = [type your answer...] - x = [type your answer...] - y = [type your answer...] - z = [type your answer...] - k = [type your answer...] **Instructions:** Fill in each box with the appropriate numeric value to complete the matrix accurately as described in your textbook's Problem 2.6. Avoid using any blank spaces in your numeric entries.
Transcribed Image Text:**Exercise: Attribute Affinity Matrix (AA) Fill-in** **Objective:** Complete the blanks to form the attribute affinity matrix (AA) based on Problem 2.6 in the textbook. Each blank must be filled with a numeric value without any spaces. **Matrix Structure:** | | A1 | A2 | A3 | A4 | A5 | |-----|----|----|----|----|----| | A1 | - | a | b | c | d | | A2 | e | - | f | g | h | | A3 | p | q | - | r | s | | A4 | t | u | v | - | w | | A5 | x | y | z | k | - | **Fill in the following:** - a = [type your answer...] - b = [type your answer...] - c = [type your answer...] - d = [type your answer...] - e = [type your answer...] - f = [type your answer...] - g = [type your answer...] - h = [type your answer...] - p = [type your answer...] - q = [type your answer...] - r = [type your answer...] - s = [type your answer...] - t = [type your answer...] - u = [type your answer...] - v = [type your answer...] - w = [type your answer...] - x = [type your answer...] - y = [type your answer...] - z = [type your answer...] - k = [type your answer...] **Instructions:** Fill in each box with the appropriate numeric value to complete the matrix accurately as described in your textbook's Problem 2.6. Avoid using any blank spaces in your numeric entries.
### Educational Resource: Matrix Representation #### Figure (a): Incidence Matrix The matrix in Figure (a) is an incidence matrix that displays the relationship between sets of elements, \( A_1, A_2, A_3, A_4, A_5 \), and \( q_1, q_2, q_3, q_4, q_5 \). Each row represents a different element \( q_i \), and each column represents an element \( A_j \). A value of '1' indicates the presence of a relationship between the corresponding elements, and '0' indicates no relationship. - **Row \( q_1 \):** \( A_2, A_3, A_5 \) - **Row \( q_2 \):** \( A_1, A_3, A_5 \) - **Row \( q_3 \):** \( A_2, A_4 \) - **Row \( q_4 \):** \( A_3 \) - **Row \( q_5 \):** \( A_1, A_2, A_3 \) #### Figure (b): Transaction Matrix The matrix in Figure (b) represents a transaction matrix showing interactions or values (\( S_1, S_2, S_3 \)) across different entities \( q_1, q_2, q_3, q_4, q_5 \). Each entry provides a quantitative representation of the relation. - **Row \( q_1 \):** \( S_1 = 10 \), \( S_2 = 20 \), \( S_3 = 0 \) - **Row \( q_2 \):** \( S_1 = 5 \), \( S_2 = 0 \), \( S_3 = 10 \) - **Row \( q_3 \):** \( S_1 = 0 \), \( S_2 = 35 \), \( S_3 = 5 \) - **Row \( q_4 \):** \( S_1 = 0 \), \( S_2 = 10 \), \( S_3 = 0 \) - **Row \( q_5 \):** \( S_1 = 0 \), \( S_2 = 15 \), \( S_3 = 0 \) This matrix can represent various scenarios
Transcribed Image Text:### Educational Resource: Matrix Representation #### Figure (a): Incidence Matrix The matrix in Figure (a) is an incidence matrix that displays the relationship between sets of elements, \( A_1, A_2, A_3, A_4, A_5 \), and \( q_1, q_2, q_3, q_4, q_5 \). Each row represents a different element \( q_i \), and each column represents an element \( A_j \). A value of '1' indicates the presence of a relationship between the corresponding elements, and '0' indicates no relationship. - **Row \( q_1 \):** \( A_2, A_3, A_5 \) - **Row \( q_2 \):** \( A_1, A_3, A_5 \) - **Row \( q_3 \):** \( A_2, A_4 \) - **Row \( q_4 \):** \( A_3 \) - **Row \( q_5 \):** \( A_1, A_2, A_3 \) #### Figure (b): Transaction Matrix The matrix in Figure (b) represents a transaction matrix showing interactions or values (\( S_1, S_2, S_3 \)) across different entities \( q_1, q_2, q_3, q_4, q_5 \). Each entry provides a quantitative representation of the relation. - **Row \( q_1 \):** \( S_1 = 10 \), \( S_2 = 20 \), \( S_3 = 0 \) - **Row \( q_2 \):** \( S_1 = 5 \), \( S_2 = 0 \), \( S_3 = 10 \) - **Row \( q_3 \):** \( S_1 = 0 \), \( S_2 = 35 \), \( S_3 = 5 \) - **Row \( q_4 \):** \( S_1 = 0 \), \( S_2 = 10 \), \( S_3 = 0 \) - **Row \( q_5 \):** \( S_1 = 0 \), \( S_2 = 15 \), \( S_3 = 0 \) This matrix can represent various scenarios
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